

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
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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



