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

%I A031934 #36 Apr 30 2024 05:47:49
%S A031934 1831,1933,2113,2221,2251,2593,2803,3121,3373,3391,3433,3643,4057,
%T A031934 4111,4567,4621,5023,5281,5623,5881,6637,6763,6841,6883,7333,7417,
%U A031934 7993,8581,8647,9013,9241,9661,9907,10273,10513,10867,10957,11197
%N A031934 Lower prime of a pair of consecutive primes having a difference of 16.
%C A031934 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
%C A031934 All terms are == 1 mod 6. - _Zak Seidov_, Mar 27 2015
%C A031934 n such that A000720(n) = A000720(n-1)+1 = A000720(n+15) = A000720(n+16)-1. - _Robert Israel_, Mar 27 2015
%H A031934 Charles R Greathouse IV, <a href="/A031934/b031934.txt">Table of n, a(n) for n = 1..10000</a>
%H A031934 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A031934 a(n) = prime(A320706(n)). - _R. J. Mathar_, Apr 30 2024
%p A031934 P:= select(isprime,[seq(2*i+1,i=1..10000)]):
%p A031934 P[select(t -> P[t+1]-P[t]=16, [$1..nops(P)-1])]; # _Robert Israel_, Mar 27 2015
%t A031934 Transpose[Select[Partition[Prime[Range[1500]], 2, 1], Last[#] - First[#] == 16 &]][[1]] (* _Bruno Berselli_, Apr 09 2013 *)
%o A031934 (Magma) [p: p in PrimesUpTo(12000) | NextPrime(p)-p eq 16]; // _Bruno Berselli_, Apr 09 2013
%o A031934 (PARI) is(n)=isprime(n) && nextprime(n+1)==n+16 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A031934 Cf. A000720, A049488, A248855.
%K A031934 nonn
%O A031934 1,1
%A A031934 _Jeff Burch_