A320705 Indices of primes followed by a gap (distance to next larger prime) of 14.

30, 62, 66, 137, 146, 150, 162, 223, 250, 283, 309, 350, 360, 382, 402, 410, 424, 434, 503, 514, 526, 532, 536, 570, 610, 649, 654, 666, 687, 704, 706, 747, 780, 790, 867, 906, 919, 929, 967, 978, 981, 992, 1011, 1023, 1038, 1042, 1057, 1072, 1133, 1154, 1160, 1177, 1184

Offset: 1

Author

M. F. Hasler, Oct 19 2018

Keywords

• nonn

Comments

Indices of the primes listed in A031932.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8000
• Index entries for primes, gaps between.

Crossrefs

Equals A000720 o A031932.

Row 7 of A174349.

Indices of 14'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..1500] | NthPrime(n+1) - NthPrime(n) eq 14]; // Vincenzo Librandi, Mar 19 2019

Mathematica

Select[Range[1500], Prime[#] + 14 == Prime[# + 1] &] (* Vincenzo Librandi, Mar 19 2019 *)
Position[Differences[Prime[Range[1200]]],14]//Flatten (* Harvey P. Dale, Nov 28 2024 *)

PARI

A(N=100,g=14,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(A031932(n)).

A320705 = { i > 0 | prime(i+1) = prime(i) + 14 }.