A255909 - OEIS

A255909

Second difference sequence of A070865.

1, 4, 2, 2, 2, 6, 2, 2, 4, 4, 4, 2, 6, 2, 2, 4, 2, 8, 6, 6, 2, 2, 2, 2, 2, 20, 6, 6, 2, 2, 8, 2, 4, 4, 2, 6, 2, 4, 4, 4, 4, 4, 4, 4, 12, 10, 2, 12, 12, 6, 8, 4, 4, 2, 8, 16, 10, 2, 18, 6, 6, 6, 2, 2, 4, 8, 2, 18, 2, 14, 4, 4, 4, 4, 10, 10, 4, 2, 10, 4, 4, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Does 2 occur infinitely many times? If so, does every even positive integer occur infinitely many times? More generally, suppose that p < q are primes, and let p(1) = p, p(2) = q, and, for n > 2, let p(n) = least prime h such that h - p(n-1) > p(n-1) - p(n-2). Does every even positive integer occur infinitely many times in the second difference sequence of (p(n))?

LINKS

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

EXAMPLE

A070865 = (2,3,5,11,19,29,41,59,79,...)

1st differences: 1,2,6,8,10,12,18,20,...

2nd differences: 1,4,2,2,2,6,2,...

MATHEMATICA

d = 0; p = 2; t = {p}; Do[d = NextPrime[p + d] - p; AppendTo[t, p += d], {200}]; t

Differences[t, 2] (* A255909 *)

(* uses Vladimir Joseph Stephan Orlovsky's program at A070865 *)

CROSSREFS

Cf. A070865, A000040.