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

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

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.

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).

Programs

Magma

[n: n in [1..2100] | NthPrime(n+1) - NthPrime(n) eq 16]; // Vincenzo Librandi, Mar 19 2019

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 *)

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

Formula

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

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