A139197 -id:A139197

A139199

Numbers k such that (k!-4)/4 is prime.

+10
20

4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Numbers k such that (k!-m)/m is prime:

for m=1 see A002982

for m=2 prime or pseudoprime see A082671

for m=3 see A139056

for m=4 see A139199

for m=5 see A139200

for m=6 see A139201

for m=7 see A139202

for m=8 see A139203

for m=9 see A139204

for m=10 see A139205

a(17) > 2000 - Ray G. Opao, Sep 30 2008

a(21) > 25000 - Robert Price, Sep 25 2016

LINKS

Table of n, a(n) for n=1..20.

MATHEMATICA

a = {}; Do[If[PrimeQ[(n! - 4)/4], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)

PROG

(PARI) is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

KEYWORD

hard,more,nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

a(15)-a(16) from Ray G. Opao, Sep 30 2008

a(17) from Serge Batalov, Feb 18 2015

a(18)-a(20) from Robert Price, Sep 25 2016

STATUS

approved

A139205

Numbers k such that (k!-10)/10 is prime.

+10
20

5, 6, 7, 11, 13, 17, 28, 81, 87, 433, 640, 647, 798, 1026, 1216, 1277, 3825, 6684

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(19) > 25000. - Robert Price, Dec 23 2016

LINKS

Table of n, a(n) for n=1..18.

MATHEMATICA

a = {}; Do[If[PrimeQ[(n! - 10)/10], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)

Select[Range[700], PrimeQ[(#!-10)/10]&] (* Harvey P. Dale, Feb 15 2015 *)

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

KEYWORD

hard,more,nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

One additional term (a(12)) from Harvey P. Dale, Feb 15 2015

More terms from Serge Batalov, Feb 18 2015

a(18) from Robert Price, Dec 23 2016

STATUS

approved

A139189

a(n) = prime(n)!-1.

+10
19

1, 5, 119, 5039, 39916799, 6227020799, 355687428095999, 121645100408831999, 25852016738884976639999, 8841761993739701954543615999999, 8222838654177922817725562879999999, 13763753091226345046315979581580902399999999, 33452526613163807108170062053440751665151999999999, 60415263063373835637355132068513997507264511999999999, 258623241511168180642964355153611979969197632389119999999999, 4274883284060025564298013753389399649690343788366813724671999999999999, 138683118545689835737939019720389406345902876772687432540821294940159999999999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers of the form (prime(n)!-m)/m :

for m=1 see A139189

for m=2 see A139190

for m=3 see A139191

for m=4 see A139192

for m=5 see A139193

for m=6 see A139194

for m=7 see A139195

for m=8 see A139196

for m=9 see A139197

for m=10 see A139198

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..85

FORMULA

a(n)=A039716(n)-1. - R. J. Mathar, May 25 2008

MATHEMATICA

Table[(Prime[n]! - 1)/1, {n, 1, 20}]

PROG

(PARI) a(n) = prime(n)!-1 \\ Charles R Greathouse IV, Apr 29 2015

(Magma) [(Factorial(NthPrime(n))-1): n in [1..20]]; // Vincenzo Librandi, Jun 02 2017

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

More terms from R. J. Mathar, May 25 2008

STATUS

approved

A139191

Natural numbers of the form (prime(n)!-3)/3.

+10
19

1, 39, 1679, 13305599, 2075673599, 118562476031999, 40548366802943999, 8617338912961658879999, 2947253997913233984847871999999, 2740946218059307605908520959999999, 4587917697075448348771993193860300799999999, 11150842204387935702723354017813583888383999999999, 20138421021124611879118377356171332502421503999999999, 86207747170389393547654785051203993323065877463039999999999, 1424961094686675188099337917796466549896781262788937908223999999999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(n)=(A139189(n+1)-2)/3. - R. J. Mathar, May 25 2008

MATHEMATICA

Table[(Prime[n]! - 3)/3, {n, 2, 20}]

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

More terms from R. J. Mathar, May 25 2008

STATUS

approved

A139190

a(n) = (prime(n)!-2)/2.

+10
18

0, 2, 59, 2519, 19958399, 3113510399, 177843714047999, 60822550204415999, 12926008369442488319999, 4420880996869850977271807999999, 4111419327088961408862781439999999, 6881876545613172523157989790790451199999999, 16726263306581903554085031026720375832575999999999, 30207631531686917818677566034256998753632255999999999, 129311620755584090321482177576805989984598816194559999999999, 2137441642030012782149006876694699824845171894183406862335999999999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..85

FORMULA

a(n) = (A139189(n)-1)/2. - R. J. Mathar, May 25 2008

MATHEMATICA

Table[(Prime[n]! - 2)/2, {n, 1, 20}]

PROG

(PARI) a(n) = (prime(n)!-2)/2 \\ Charles R Greathouse IV, Apr 29 2015

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

More terms from R. J. Mathar, May 25 2008

STATUS

approved

A139192

a(n) = (prime(n)! - 4)/4.

+10
18

29, 1259, 9979199, 1556755199, 88921857023999, 30411275102207999, 6463004184721244159999, 2210440498434925488635903999999, 2055709663544480704431390719999999, 3440938272806586261578994895395225599999999, 8363131653290951777042515513360187916287999999999, 15103815765843458909338783017128499376816127999999999, 64655810377792045160741088788402994992299408097279999999999, 1068720821015006391074503438347349912422585947091703431167999999999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 3..87

FORMULA

a(n) = (A139189(n+2) - 3)/4. - R. J. Mathar, May 25 2008

MATHEMATICA

Table[(Prime[n]! - 4)/4, {n, 3, 20}]

PROG

(Magma) [(Factorial(NthPrime(n))-4)/4: n in [3..20]]; // Vincenzo Librandi, Jun 02 2017

(PARI) a(n) = (prime(n)!-4)/4;

lista(nn) = for (n=3, nn, print1(a(n), ", ")); \\ Michel Marcus, Feb 17 2018

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

More terms from R. J. Mathar, May 25 2008

STATUS

approved

A139193

Natural numbers of the form (prime(n)! - 5)/5.

+10
18

23, 1007, 7983359, 1245404159, 71137485619199, 24329020081766399, 5170403347776995327999, 1768352398747940390908723199999, 1644567730835584563545112575999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..9.

MAPLE

A039716 := proc(n) factorial(ithprime(n)) ; end: A139193 := proc(n) A039716(n)/5-1 ; end: seq(A139193(n), n=3..14) ; # R. J. Mathar, Sep 18 2009

MATHEMATICA

Table[(Prime[n]! - 5)/5, {n, 3, 20}]

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

STATUS

approved

A139194

Natural numbers of the form (prime(n)!-6)/6.

+10
18

0, 19, 839, 6652799, 1037836799, 59281238015999, 20274183401471999, 4308669456480829439999, 1473626998956616992423935999999, 1370473109029653802954260479999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..10.

MATHEMATICA

Table[(Prime[n]! - 6)/6, {n, 2, 20}]

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

STATUS

approved

A139195

(prime(n)!-7)/7.

+10
18

719, 5702399, 889574399, 50812489727999, 17377871486975999, 3693145248412139519999, 1263108856248528850649087999999, 1174691236311131831103651839999999, 1966250441603763578045139940225843199999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

4,1

COMMENTS

Not an integer for n < 4.

LINKS

Table of n, a(n) for n=4..12.

MATHEMATICA

Table[(Prime[n]! - 7)/7, {n, 4, 20}]

CROSSREFS

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

Edited with one more term by Franklin T. Adams-Watters, Apr 09 2009

STATUS

approved

A139196

a(n) = (prime(n)!-8)/8.

+10
18

14, 629, 4989599, 778377599, 44460928511999, 15205637551103999, 3231502092360622079999, 1105220249217462744317951999999, 1027854831772240352215695359999999, 1720469136403293130789497447697612799999999

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,1

LINKS

Table of n, a(n) for n=3..12.

FORMULA

a(n) = (A039716(n) - 8)/8. - Elmo R. Oliveira, Jan 20 2023

MATHEMATICA

Table[(Prime[n]! - 8)/8, {n, 3, 20}]

CROSSREFS

Cf. A039716, A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 11 2008

EXTENSIONS

Edited by Max Alekseyev, Sep 15 2009

STATUS

approved