A031932 Lower prime of a pair of consecutive primes having a difference of 14.

113, 293, 317, 773, 839, 863, 953, 1409, 1583, 1847, 2039, 2357, 2423, 2633, 2753, 2819, 2939, 3023, 3593, 3677, 3779, 3833, 3863, 4139, 4493, 4817, 4889, 4973, 5153, 5309, 5333, 5669, 5939, 6053, 6719, 7043, 7193, 7283, 7607, 7703

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between

Formula

a(n) = prime(A320705(n)). - R. J. Mathar, Apr 30 2024

Mathematica

Transpose[Select[Partition[Prime[Range[1000]], 2, 1], Last[#]-First[#] == 14&]] [[1]] (* Harvey P. Dale, Aug 24 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(8000) | NextPrime(p)-p eq 14]; // Bruno Berselli, Apr 09 2013
(PARI) is(n)=isprime(n) && nextprime(n+1)==n+14 \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

Subsequence of A124586.

Cf. A248855.

Sequence in context: A059331 A124586 A051110 * A216310 A211445 A172983

Adjacent sequences: A031929 A031930 A031931 * A031933 A031934 A031935

Keyword

nonn

Author

Jeff Burch

Status

approved