A237816 k such that either 2^k + k - 3 or 2^k + k - 2 is prime.

2, 4, 6, 10, 70, 82, 143, 150, 220, 413, 426, 816, 5497, 6649, 7429, 7728, 7891, 8248, 14567, 15522, 17935, 24942, 37415, 123773

Offset: 1

Author

Robin Garcia, Feb 13 2014

Keywords

• nonn
• more

Comments

Numbers of this form can be represented in the numeral system described in A235860 with k - 1 ones followed to the right by k - 1 twos or k ones followed to the right by k - 1 twos, like this: 1, 12, 112, 1122, 11122, 111222, 1111222, ... (1, 3, 4, 8, 9, 17, 18, ... in decimal) and are the least numbers that need one more digit to be represented than any of their predecessors.

The corresponding sequence of primes starts 3, 17, 67, 1031, 1180591620717411303491, ...

Crossrefs

Cf. A235860, A236547.

Programs

Mathematica

 fQ[n_] := PrimeQ[2^n + n - If[ OddQ@ n, 2, 3]]; Select[ Range@ 30000, fQ]

PARI

isok(n) = isprime(2^n + n - 3) || isprime(2^n + n - 2); \\ Michel Marcus, Feb 13 2014

Extensions

a(21)-a(22) from Robert G. Wilson v, Mar 03 2014

a(23) from Michael S. Branicky, May 01 2023

a(24) from Michael S. Branicky, Jul 30 2024