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

1,1

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.

Formula

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

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

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 *)

Prog

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

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).

Sequence in context: A108303 A062695 A107730 * A095419 A232581 A039417

Adjacent sequences: A320700 A320701 A320702 * A320704 A320705 A320706

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved