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

Offset: 1

Author

Clark Kimberling, Apr 14 2015

Keywords

• nonn
• easy

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))?

Examples

			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,...
		

Links

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

Crossrefs

Cf. A070865, A000040.

Programs

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 *)