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

1,1

Comments

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.

Links

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

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A219096.

Sequence in context: A040430 A040432 A035419 * A040433 A317321 A080472

Adjacent sequences: A218246 A218247 A218248 * A218250 A218251 A218252

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2013

Status

approved