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%I #34 Sep 08 2022 08:44:50
%S 1831,1933,2113,2221,2251,2593,2803,3121,3373,3391,3433,3643,4057,
%T 4111,4567,4621,5023,5281,5623,5881,6637,6763,6841,6883,7333,7417,
%U 7993,8581,8647,9013,9241,9661,9907,10273,10513,10867,10957,11197
%N Lower prime of a pair of consecutive primes having a difference of 16.
%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
%C All terms are == 1 mod 6. - _Zak Seidov_, Mar 27 2015
%C n such that A000720(n) = A000720(n-1)+1 = A000720(n+15) = A000720(n+16)-1. - _Robert Israel_, Mar 27 2015
%H Charles R Greathouse IV, <a href="/A031934/b031934.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%p P:= select(isprime,[seq(2*i+1,i=1..10000)]):
%p P[select(t -> P[t+1]-P[t]=16, [$1..nops(P)-1])]; # _Robert Israel_, Mar 27 2015
%t Transpose[Select[Partition[Prime[Range[1500]], 2, 1], Last[#] - First[#] == 16 &]][[1]] (* _Bruno Berselli_, Apr 09 2013 *)
%o (Magma) [p: p in PrimesUpTo(12000) | NextPrime(p)-p eq 16]; // _Bruno Berselli_, Apr 09 2013
%o (PARI) is(n)=isprime(n) && nextprime(n+1)==n+16 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A000720, A049488, A248855.
%K nonn
%O 1,1
%A _Jeff Burch_
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