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

Offset

1,1

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, ...

Links

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

Mathematica

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

Prog

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

Crossrefs

Cf. A235860, A236547.

Sequence in context: A073308 A058960 A036053 * A088906 A303752 A304532

Adjacent sequences: A237813 A237814 A237815 * A237817 A237818 A237819

Keyword

nonn,more

Author

Robin Garcia, 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

Status

approved