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A255909
Second difference sequence of A070865.
1
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
1,2
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
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
Sequence in context: A129107 A341686 A353636 * A344903 A198101 A364686
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2015
STATUS
approved