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%I #35 Oct 21 2022 22:13:10
%S 89,359,389,401,449,479,491,683,701,719,743,761,911,929,983,1109,1163,
%T 1193,1373,1439,1523,1559,1571,1733,1823,1979,2003,2153,2213,2243,
%U 2273,2459,2531,2609,2663,2699,2741,2843,2879,2909,3011,3041
%N Lower prime of a difference of 8 between consecutive primes.
%C 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
%H Charles R Greathouse IV, <a href="/A031926/b031926.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 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 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
%t Transpose[Select[Partition[Prime[Range[500]], 2, 1], Last[#] - First[#] == 8 &]][[1]] (* _Bruno Berselli_, Apr 09 2013 *)
%o (Magma) [p: p in PrimesUpTo(4000) | NextPrime(p)-p eq 8]; // _Bruno Berselli_, Apr 09 2013
%o (PARI) is_A031926(p)={precprime(p-1)==p-8 && isprime(p)} \\ _M. F. Hasler_, Apr 20 2013
%o (PARI) q=0;forprime(p=1,5000,q+8==(q=p)&&print1(p-8",")) \\ _M. F. Hasler_, Apr 20 2013
%Y Cf. A023202.
%K nonn
%O 1,1
%A _Jeff Burch_
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