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

1,1

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

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 *)

Prog

(Magma) [p: p in PrimesUpTo(12000) | NextPrime(p)-p eq 16]; // Bruno Berselli, Apr 09 2013
(PARI) is(n)=isprime(n) && nextprime(n+1)==n+16 \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Cf. A000720, A049488, A248855.

Sequence in context: A205921 A196895 A151644 * A020423 A031804 A054813

Adjacent sequences: A031931 A031932 A031933 * A031935 A031936 A031937

Keyword

nonn

Author

Jeff Burch

Status

approved