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A031934
Lower prime of a pair of consecutive primes having a difference of 16.
12
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
FORMULA
a(n) = prime(A320706(n)). - R. J. Mathar, Apr 30 2024
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
KEYWORD
nonn
AUTHOR
STATUS
approved