A270711 Half of increasing gaps between primes.

1, 2, 3, 4, 7, 9, 10, 11, 17, 18, 22, 26, 36, 43, 48, 56, 57, 59, 66, 74, 77, 90, 105, 110, 111, 117, 124, 125, 141, 144, 146, 160, 168, 177, 191, 192, 197, 228, 232, 234, 237, 243, 245, 250, 257, 258, 266, 267, 270, 291, 294, 301, 326, 337, 358, 383, 389, 402, 403, 453, 458, 462, 566, 592, 599, 610, 612, 624, 636, 664, 678, 685, 721, 738, 744, 755, 763, 765, 775

Offset: 2

Author

Michel Lagneau, Mar 22 2016

Keywords

• nonn

Comments

The primes in this sequence are 2, 3, 7, 11, 17, 43, 59, 191, 197, 257, ...

The squares are 1, 4, 9, 36, 144,...

Crossrefs

Cf. A005250.

Programs

Mathematica

max = 10^7; Module[{d = Differences[Prime[Range[max]]], ls = {2}}, Table[If[d[[n]] > Last[ls], AppendTo[ls, d[[n]]]], {n, max - 1}]; ls/2]

Formula

a(n) = A005250(n)/2 for n>1.

Extensions

a(55)-a(80) using b-file of A005250 by Hugo Pfoertner, Oct 30 2021