A320719 Indices of primes followed by a gap (distance to next larger prime) of 42.

1879, 3732, 4059, 4135, 4714, 5355, 5948, 6160, 6841, 7434, 7724, 7746, 7952, 7980, 8081, 8269, 8580, 9303, 9395, 9971, 10045, 10305, 10968, 11023, 11135, 11251, 11338, 11399, 11515, 11807, 11888, 11901, 12089, 12374, 12488, 13277, 13447, 14497, 14802, 15086, 15089, 15350, 15612, 15785

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes listed in A134120.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..3000
• Index entries for primes, gaps between.

Crossrefs

Cf. A029707, A029709 (analog for gaps 2 & 4), A320701, A320702, ... A320720 (analog for gaps 6, 8, ..., 44), A116493 (gap 70), A116496 (gap 100), A116497 (gap 200), A116495 (gap 210).

Equals A000720 o A134120.

Indices of 42's in A001223.

Row 21 of A174349.

Programs

Mathematica

Position[Differences[Prime[Range[16000]]],42]//Flatten (* Harvey P. Dale, Feb 22 2020 *)

PARI

A(N=100,g=42,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(A134120(n)).