A320709 Indices of primes followed by a gap (distance to next larger prime) of 22.

189, 297, 344, 375, 457, 487, 522, 549, 557, 721, 836, 914, 1010, 1158, 1170, 1197, 1233, 1242, 1272, 1290, 1370, 1390, 1444, 1471, 1625, 1633, 1672, 1683, 1757, 1858, 1975, 1983, 2039, 2074, 2158, 2243, 2248, 2250, 2327, 2370, 2388, 2614, 2638, 2703, 2725, 2838, 2842, 2872

Offset

1,1

Comments

Indices of the primes listed in A061779.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10040

Index entries for primes, gaps between.

Formula

a(n) = A000720(A061779(n)).

A320709 = { i > 0 | prime(i+1) = prime(i) + 22 }.

Mathematica

Select[Range[3000], Prime[#] + 22 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 22 2019 *)

Prog

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

Crossrefs

Equals A000720 o A061779.

Row 11 of A174349.

Indices of 22's in A001223.

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).

Sequence in context: A253024 A031901 A348160 * A224674 A076759 A348544

Adjacent sequences: A320706 A320707 A320708 * A320710 A320711 A320712

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved