login
A320703
Indices of primes followed by a gap (distance to next larger prime) of 10.
6
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.
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 19 2018
STATUS
approved