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Indices of primes followed by a gap (distance to next larger prime) of 20.
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%I #15 Sep 08 2022 08:46:23

%S 154,259,442,480,548,753,777,783,876,971,1035,1066,1095,1106,1147,

%T 1254,1277,1302,1337,1345,1355,1381,1396,1400,1423,1438,1562,1592,

%U 1613,1662,1669,1808,1955,2016,2043,2081,2116,2129,2147,2226,2302,2307,2387,2517,2547,2563,2694,2724,2745,2755,2766

%N Indices of primes followed by a gap (distance to next larger prime) of 20.

%C Indices of the primes listed in A031938.

%H Vincenzo Librandi, <a href="/A320708/b320708.txt">Table of n, a(n) for n = 1..10720</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.

%F a(n) = A000720(A031938(n)).

%F A320708 = { i > 0 | prime(i+1) = prime(i) + 20 } = A001223^(-1)({20}).

%t Select[Range[3000], Prime[#] + 20 == Prime[# + 1] &] (* _Vincenzo Librandi_, Mar 22 2019 *)

%o (PARI) A(N=100,g=20,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 (Magma) [n: n in [1..3000] | NthPrime(n+1) - NthPrime(n) eq 20]; // _Vincenzo Librandi_, Mar 22 2019

%Y Equals A000720 o A031938.

%Y Row 10 of A174349.

%Y Subsequence of A107730 (prime(n+1) ends in same digit as prime(n)).

%Y Indices of 20's in A001223.

%Y 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 nonn

%O 1,1

%A _M. F. Hasler_, Oct 19 2018