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