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A218249 Difference sequence of A219096. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 13:27 EDT 2019. Contains 328089 sequences. (Running on oeis4.)