A033875 Skipping from prime to prime by least powers of 2.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 79, 83, 211, 227, 229, 233, 241, 257, 769, 773

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Is this sequence infinite? - Charles R Greathouse IV, Jan 24 2017

Examples

			2 + 2^0 = 3,
3 + 2^1 = 5,
a(22) = a(21) + 2^955,
a(23) = a(22) + 2^468.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..23

Crossrefs

Cf. A059661, A067760, A139803 (corresponding powers of 2).

Programs

Mathematica

NestList[(k = 0; While[! PrimeQ[q = # + 2^k], k++]; q) &, 2, 20] (* Zak Seidov, Jan 24 2017 *)

Formula

a(1) = 2, a(n+1) = a(n) + 2^k; a(n+1) prime, k minimal.

a(n) = a(n-1) + 2^A067760((a(n-1)-1)/2) for n >= 3. - Pontus von Brömssen, Jan 08 2023