A219096 -id:A219096 - cp's OEIS frontend

A218249 Difference sequence of A219096.

21, 3, 15, 1, 18, 29, 5, 3, 8, 11, 31, 4, 20, 3, 7, 5, 19, 53, 1, 19, 48, 19, 29, 32, 7, 38, 1, 43, 12, 33, 52, 16, 8, 38, 15, 1, 19, 7, 1, 23, 28, 30, 22, 8, 1, 7, 1, 52, 14, 56, 10, 26, 32, 65, 5, 71, 12, 83, 37, 6

Offset: 1

Clark Kimberling, Mar 26 2013

Each appearance of 1 represents a prime p for which the next 3 larger primes are p+6, p+12, and p+18. More generally, the sequence gives gap sizes, measured as the number of primes minus 1, between consecutive triples (p, p+6, p+12) and (q, q+6, q+12) of consecutive primes. Conjecture: Every positive integer except 2 occurs infinitely many times.

			A219096 = (15, 36, 39, 54, 55, 73, ...), so that
A218249 = (21, 3, 15, 1, 18, 29, 5, ...).
The first 1 in A218249 represents the primes p(54)=251, p(55)=257, P(56)=263, P(57)=269.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A219096.

z = 10000; t = Differences[Prime[Range[z]]];
f[n_] := If[t[[n + 1]] - t[[n]] == 0, t[[n]], 0]
u = Table[f[n], {n, 1, 5000}];
p = Flatten[Position[u, 6]] (* A219096 *)
Flatten[Differences[p]] (* A218249 *)

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A218249 Difference sequence of A219096.

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