The On-Line Encyclopedia of Integer Sequences (OEIS)

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A118377

a(n) is the least prime p such that prime(n)# * p# - 1 is prime.
(history; published version)

#10 by Peter Luschny at Sat Sep 11 10:47:34 EDT 2021

STATUS

reviewed

approved

#9 by Joerg Arndt at Sat Sep 11 08:18:34 EDT 2021

STATUS

proposed

reviewed

#8 by Michel Marcus at Sat Sep 11 06:49:19 EDT 2021

STATUS

editing

proposed

#7 by Michel Marcus at Sat Sep 11 06:49:10 EDT 2021

PROG

(PARI) pr(p) = my(pr=1); forprime(q=2, p, pr *= q); pr;

a(n) = my(p=2, P=pr(prime(n))); while (!ispseudoprime(P*pr(p)-1), p = nextprime(p+1)); p; \\ Michel Marcus, Sep 11 2021

STATUS

proposed

editing

Discussion

Sat Sep 11

06:49

Michel Marcus: yes same terms

#6 by Amiram Eldar at Sat Sep 11 05:53:55 EDT 2021

STATUS

editing

proposed

#5 by Amiram Eldar at Sat Sep 11 05:30:07 EDT 2021

EXAMPLE

2*2-1 = 3 is prime , 2 = p(1)# , so a(1) = 2.

2*3*2-1 = 11 is prime , 2*3 = p(2)# , so a(2) = 2.

2*3*5*2-1 = 59 is prime , 2*3*5 = p(3)# , so a(3) = 2.

2*3*5*7*2-1 = 419 is prime , 2*3*5*7 = p(4)# , so a(4) = 2.

2*3*5*7*11*2*3-1 = 13859 is prime , 2*3*5*7*11 = p(5)# , so a(5) = 3.

CROSSREFS

Cf. A002110.

#4 by Amiram Eldar at Sat Sep 11 05:28:03 EDT 2021

NAME

Least a(n) is the least prime p such that pprime(n)# * p# - 1 is prime.

DATA

2, 2, 2, 2, 3, 3, 2, 2, 13, 3, 13, 2, 3, 11, 7, 37, 151, 11, 113, 2, 5, 2, 401, 73, 7, 109, 3, 7, 101, 2, 11, 109, 5, 277, 11, 7, 31, 89, 191, 31, 11, 2713, 11, 13, 73, 461, 17, 17, 5, 41, 257, 17, 127, 1307, 53, 71, 281, 829, 139, 269, 137, 7, 41, 19, 107, 89

MATHEMATICA

pr[n_] := Product[Prime[i], {i, 1, n}]; a[n_] := Module[{prn = pr[n], k = 1}, While[!PrimeQ[prn*pr[k] - 1], k++]; Prime[k]]; Array[a, 50] (* Amiram Eldar, Sep 11 2021 *)

EXTENSIONS

More terms from Amiram Eldar, Sep 11 2021

STATUS

approved

editing

#3 by Russ Cox at Sat Mar 31 13:22:04 EDT 2012

AUTHOR

_Pierre CAMI (pierre-cami(AT)bbox.fr), _, May 15 2006

Discussion

Sat Mar 31

13:22

OEIS Server: https://oeis.org/edit/global/885

#2 by Charles R Greathouse IV at Thu Dec 01 11:14:25 EST 2011

AUTHOR

Pierre CAMI (pierrecamipierre-cami(AT)tele2bbox.fr), May 15 2006

Discussion

Thu Dec 01

11:14

OEIS Server: https://oeis.org/edit/global/101

#1 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

NAME

Least prime p such that p(n)#*p#-1 is prime.

DATA

2, 2, 2, 2, 3, 3, 2, 2, 13, 3, 13, 2, 3, 11, 7, 37, 151, 11, 113, 2, 5, 2, 401, 73, 7, 109, 3, 7, 101, 2, 11, 109, 5, 277, 11, 7, 31, 89, 191, 31, 11, 2713, 11, 13, 73, 461

OFFSET

1,1

EXAMPLE

2*2-1=3 prime 2=p(1)# so a(1)=2

2*3*2-1=11 prime 2*3=p(2)# so a(2)=2

2*3*5*2-1=59 prime 2*3*5=p(3)# so a(3)=2

2*3*5*7*2-1=419 prime 2*3*5*7=p(4)# so a(4)=2

2*3*5*7*11*2*3-1=13859 prime 2*3*5*7*11=p(5)# so a(5)=3

KEYWORD

nonn,new

AUTHOR

Pierre CAMI (pierrecami(AT)tele2.fr), May 15 2006

STATUS

approved