A320706 -id:A320706 - cp's OEIS frontend

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

Jeff Burch

nonn

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

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

Cf. A000720, A049488, A248855.

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

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

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

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

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

cp's OEIS Frontend

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

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