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Search: a139196 -id:a139196
Displaying 1-10 of 17 results found.
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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
A139197
Natural numbers of the form (prime(n)!-9)/9.
+10
18
559, 4435199, 691891199, 39520825343999, 13516122267647999, 2872446304320552959999, 982417999304411328282623999999, 913648739353102535302840319999999
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..8.
MATHEMATICA
Table[(Prime[n]! - 9)/9, {n, 4, 20}]
(Prime[Range[4, 20]]!-9)/9 (* Harvey P. Dale, Apr 10 2019 *)
CROSSREFS
Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.
KEYWORD
nonn
AUTHOR
Artur Jasinski, Apr 11 2008
STATUS
approved
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