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%I #33 Apr 30 2024 05:48:37
%S 113,293,317,773,839,863,953,1409,1583,1847,2039,2357,2423,2633,2753,
%T 2819,2939,3023,3593,3677,3779,3833,3863,4139,4493,4817,4889,4973,
%U 5153,5309,5333,5669,5939,6053,6719,7043,7193,7283,7607,7703
%N Lower prime of a pair of consecutive primes having a difference of 14.
%C 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
%H Charles R Greathouse IV, <a href="/A031932/b031932.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F a(n) = prime(A320705(n)). - _R. J. Mathar_, Apr 30 2024
%t Transpose[Select[Partition[Prime[Range[1000]],2,1],Last[#]-First[#] == 14&]] [[1]] (* _Harvey P. Dale_, Aug 24 2012 *)
%o (Magma) [p: p in PrimesUpTo(8000) | NextPrime(p)-p eq 14]; // _Bruno Berselli_, Apr 09 2013
%o (PARI) is(n)=isprime(n) && nextprime(n+1)==n+14 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Subsequence of A124586.
%Y Cf. A248855.
%K nonn
%O 1,1
%A _Jeff Burch_
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