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A320714 Indices of primes followed by a gap (distance to next larger prime) of 32.

%I A320714 #15 Jun 19 2024 17:49:31
%S A320714 738,1315,3022,3042,3607,4112,4300,4362,4555,4619,4761,4893,5204,5358,
%T A320714 5615,5637,6215,6265,6479,6610,6706,6933,7295,7829,7884,8049,8198,
%U A320714 8548,9085,9155,9524,9588,9641,9826,9924,10463,10824,11367,11590,11701,11729,11869,12159,12258,12275,12327
%N A320714 Indices of primes followed by a gap (distance to next larger prime) of 32.
%C A320714 Indices of the primes listed in A126784.
%H A320714 Robert Israel, <a href="/A320714/b320714.txt">Table of n, a(n) for n = 1..10000</a>
%H A320714 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%F A320714 a(n) = A000720(A126784(n)).
%F A320714 A320714 = { i>0 | prime(i+1) = prime(i) + 32 }.
%p A320714 p:= 2: Res:= NULL: count:= 0:
%p A320714 for k from 1 while count < 100 do
%p A320714   q:= nextprime(p);
%p A320714   if q - p = 32 then
%p A320714     count:= count+1;
%p A320714     Res:= Res, k;
%p A320714   fi;
%p A320714   p:= q;
%p A320714 od:
%p A320714 Res; # _Robert Israel_, Oct 25 2018
%t A320714 PrimePi/@Select[Partition[Prime[Range[15000]],2,1],#[[2]]-#[[1]]==32&][[;;,1]] (* _Harvey P. Dale_, Jun 19 2024 *)
%o A320714 (PARI) A(N=100,g=32,p=2,i=primepi(p)-1,L=List())={forprime(q=1+p,,i++; if(p+g==p=q, listput(L,i); N--||break));Vec(L)} \\ returns the list of first N terms of the sequence
%Y A320714 Equals A000720 o A126784.
%Y A320714 Indices of 32's in A001223.
%Y A320714 Row 16 of A174349.
%Y A320714 Cf. A029707, A029709, A320701, A320702, ..., A320720 (analog for gaps 2, 4, 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).
%K A320714 nonn
%O A320714 1,1
%A A320714 _M. F. Hasler_, Oct 19 2018