A031934 Lower prime of a pair of consecutive primes having a difference of 16.

1831, 1933, 2113, 2221, 2251, 2593, 2803, 3121, 3373, 3391, 3433, 3643, 4057, 4111, 4567, 4621, 5023, 5281, 5623, 5881, 6637, 6763, 6841, 6883, 7333, 7417, 7993, 8581, 8647, 9013, 9241, 9661, 9907, 10273, 10513, 10867, 10957, 11197

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n); i.e., a(n)^(1/n) is a strictly decreasing function of n (see comment lines of the sequence A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

All terms are == 1 mod 6. - Zak Seidov, Mar 27 2015

n such that A000720(n) = A000720(n-1)+1 = A000720(n+15) = A000720(n+16)-1. - Robert Israel, Mar 27 2015

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for primes, gaps between

Crossrefs

Cf. A000720, A049488, A248855.

Programs

Magma

[p: p in PrimesUpTo(12000) | NextPrime(p)-p eq 16]; // Bruno Berselli, Apr 09 2013

Maple

P:= select(isprime,[seq(2*i+1,i=1..10000)]):
P[select(t -> P[t+1]-P[t]=16, [$1..nops(P)-1])]; # Robert Israel, Mar 27 2015

Mathematica

Transpose[Select[Partition[Prime[Range[1500]], 2, 1], Last[#] - First[#] == 16 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

PARI

is(n)=isprime(n) && nextprime(n+1)==n+16 \\ Charles R Greathouse IV, Sep 14 2015

Formula

a(n) = prime(A320706(n)). - R. J. Mathar, Apr 30 2024