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A320703 Indices of primes followed by a gap (distance to next larger prime) of 10.

%I A320703 #17 Sep 08 2022 08:46:23
%S A320703 34,42,53,61,68,80,82,101,106,115,125,127,138,141,145,157,172,175,177,
%T A320703 191,193,204,222,233,258,266,269,279,289,306,308,310,316,324,369,383,
%U A320703 397,399,403,418,422,431,443,474,491,497,500,502,518,525,531,535,575
%N A320703 Indices of primes followed by a gap (distance to next larger prime) of 10.
%C A320703 Indices of the primes given in A031928.
%H A320703 Vincenzo Librandi, <a href="/A320703/b320703.txt">Table of n, a(n) for n = 1..8870</a>
%H A320703 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%F A320703 a(n) = A000720(A031928(n)).
%F A320703 A320703 = { i > 0 | prime(i+1) = prime(i) + 10 }.
%t A320703 Select[Range[1000], Prime[#] + 10 == Prime[# + 1] &] (* _Vincenzo Librandi_, Mar 21 2019 *)
%t A320703 Position[Partition[Prime[Range[600]],2,1],_?(#[[2]]-#[[1]]==10&),1,Heads-> False]//Flatten (* _Harvey P. Dale_, Mar 08 2020 *)
%o A320703 (PARI) A320703_vec(N=100,g=10,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
%o A320703 (Magma) [n: n in [1..1000] | NthPrime(n+1) - NthPrime(n) eq 10]; // _Vincenzo Librandi_, Mar 21 2019
%Y A320703 Equals A000720 o A031928.
%Y A320703 Row 5 of A174349.
%Y A320703 Indices of 10's in A001223.
%Y A320703 Subsequence of A107730: prime(n+1) ends in same digit as prime(n).
%Y A320703 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 A320703 nonn
%O A320703 1,1
%A A320703 _M. F. Hasler_, Oct 19 2018