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A031934 Lower prime of a pair of consecutive primes having a difference of 16. 9
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 (list; graph; refs; listen; history; text; internal format)
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

Index entries for primes, gaps between

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

Cf. A000720, A049488, A248855.

Sequence in context: A205921 A196895 A151644 * A020423 A031804 A054813

Adjacent sequences:  A031931 A031932 A031933 * A031935 A031936 A031937

KEYWORD

nonn

AUTHOR

Jeff Burch

STATUS

approved

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Last modified May 28 20:12 EDT 2017. Contains 287241 sequences.