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

34, 42, 53, 61, 68, 80, 82, 101, 106, 115, 125, 127, 138, 141, 145, 157, 172, 175, 177, 191, 193, 204, 222, 233, 258, 266, 269, 279, 289, 306, 308, 310, 316, 324, 369, 383, 397, 399, 403, 418, 422, 431, 443, 474, 491, 497, 500, 502, 518, 525, 531, 535, 575

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes given in A031928.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8870
• Index entries for primes, gaps between.

Crossrefs

Equals A000720 o A031928.

Row 5 of A174349.

Indices of 10's in A001223.

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

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).

Programs

Magma

[n: n in [1..1000] | NthPrime(n+1) - NthPrime(n) eq 10]; // Vincenzo Librandi, Mar 21 2019

Mathematica

Select[Range[1000], Prime[#] + 10 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 21 2019 *)
Position[Partition[Prime[Range[600]],2,1],?(#[[2]]-#[[1]]==10&),1,Heads-> False]//Flatten (* _Harvey P. Dale, Mar 08 2020 *)

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

Formula

a(n) = A000720(A031928(n)).

A320703 = { i > 0 | prime(i+1) = prime(i) + 10 }.