A320706 Indices of primes followed by a gap (distance to next larger prime) of 16.

282, 295, 319, 331, 335, 378, 409, 445, 476, 478, 481, 510, 560, 566, 619, 624, 674, 701, 739, 775, 856, 871, 881, 886, 935, 941, 1007, 1069, 1077, 1121, 1146, 1193, 1222, 1261, 1286, 1322, 1331, 1356, 1372, 1388, 1405, 1460, 1487, 1500, 1587, 1603, 1608, 1612, 1699, 1719, 1734, 1740, 1811, 1876, 1924, 1956, 1969, 1977, 2002, 2022, 2034, 2042, 2071

Offset

1,1

Comments

Indices of the primes listed in A031934.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..9790

Index entries for primes, gaps between.

Formula

a(n) = A000720(A031934(n)).

A320706 = { i > 0 | prime(i+1) = prime(i) + 16 }.

Mathematica

Select[Range[2500], Prime[#] + 16 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 19 2019 *)
Position[Partition[Prime[Range[2100]], 2, 1], _?(#[[2]]-#[[1]]== 16&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Nov 01 2020 *)

Prog

(PARI) A(N=100, g=16, 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..2100] | NthPrime(n+1) - NthPrime(n) eq 16]; // Vincenzo Librandi, Mar 19 2019

Crossrefs

Equals A000720 o A031934.

Row 8 of A174349.

Indices of 16'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: A185710 A242982 A255387 * A356854 A114804 A250580

Adjacent sequences: A320703 A320704 A320705 * A320707 A320708 A320709

Keyword

nonn

Author

M. F. Hasler, Oct 19 2018

Status

approved