A031926 Lower prime of a difference of 8 between consecutive primes.

89, 359, 389, 401, 449, 479, 491, 683, 701, 719, 743, 761, 911, 929, 983, 1109, 1163, 1193, 1373, 1439, 1523, 1559, 1571, 1733, 1823, 1979, 2003, 2153, 2213, 2243, 2273, 2459, 2531, 2609, 2663, 2699, 2741, 2843, 2879, 2909, 3011, 3041

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n). Namely 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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index entries for primes, gaps between

Crossrefs

Cf. A023202.

Programs

Magma

[p: p in PrimesUpTo(4000) | NextPrime(p)-p eq 8]; // Bruno Berselli, Apr 09 2013

Maple

for i from 1 to 446 do if ithprime(i+1) = ithprime(i) + 8 then print({ithprime(i)}); fi; od; # Zerinvary Lajos, Mar 19 2007
p:=ithprime; nx:=nextprime; f:=proc(d) global p,nx; local i,t0,n; t0:=[]; for n from 1 to 100000 do i:=p(n); if nx(i)-i=d then t0:=[op(t0),i]; fi; od: t0; end; f(8); # N. J. A. Sloane, Jan 17 2012

Mathematica

Transpose[Select[Partition[Prime[Range[500]], 2, 1], Last[#] - First[#] == 8 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

PARI

is_A031926(p)={precprime(p-1)==p-8 && isprime(p)} \\ M. F. Hasler, Apr 20 2013

PARI

q=0;forprime(p=1,5000,q+8==(q=p)&&print1(p-8",")) \\ M. F. Hasler, Apr 20 2013