A066513 Numbers n such that f(n) = f(n-1) - f(n-2) where f is the prime gap function given by f(m) = prime(m+1) - prime(m) and prime(m) denotes the m-th prime.

5, 7, 10, 12, 19, 22, 28, 33, 45, 52, 59, 63, 81, 85, 92, 95, 115, 136, 138, 140, 144, 147, 171, 192, 198, 209, 211, 222, 224, 236, 249, 253, 256, 268, 270, 279, 288, 315, 318, 322, 325, 348, 355, 358, 373, 400

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Mathematica

f[x_] := Prime[x + 1] - Prime[x]; Select[Range[3, 10^3], f[ # ] == f[ # - 1] - f[ # - 2] &]
Flatten[Position[Partition[Differences[Prime[Range[500]]], 3, 1], _?(#[[3]] == #[[2]]-#[[1]]&), 1, Heads->False]]+2 (* Harvey P. Dale, Mar 19 2019 *)

Prog

(PARI) Gap(m) = { return(prime(m+1) - prime(m)); }
{ n=0; for (m=3, 10^10, if (Gap(m) == Gap(m-1) - Gap(m-2), write("b066513.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 20 2010

Crossrefs

Cf. A001223 (f).

Sequence in context: A256680 A293867 A129189 * A218852 A028810 A097700

Adjacent sequences: A066510 A066511 A066512 * A066514 A066515 A066516

Keyword

nonn

Author

Joseph L. Pe, Jan 04 2002

Status

approved