A301744 Numbers k such that 2^k - 2*k + 1 is prime.

0, 3, 5, 6, 8, 11, 12, 13, 18, 25, 31, 35, 114, 152, 186, 228, 245, 308, 360, 371, 575, 685, 721, 732, 1361, 2394, 3138, 3446, 5964, 9482, 22793, 51233, 112800, 120491, 199615, 416641

Offset: 1

Author

Vaclav Kotesovec, Mar 26 2018

Keywords

• nonn
• more
• hard

Comments

Terms through 1361 correspond to provable primes; terms beyond 1361 correspond to probable primes.

After 22793, there are no more terms through 40000. - Jon E. Schoenfield, Mar 27 2018

a(37) > 5*10^5. - Robert Price, Jun 01 2018

Crossrefs

Cf. A100359, A100361, A301634.

Programs

Magma

[n: n in [0..1000] |IsPrime(2^n-2*n+1)]; // Vincenzo Librandi, Mar 27 2018

Maple

select(k->isprime(2^k-2*k+1),[$0..3000]); # Muniru A Asiru, Apr 03 2018

Mathematica

Select[Range[0, 1000], PrimeQ[2^# - 2*# + 1] &]

PARI

isok(n) = isprime(2^n-2*n+1); \\ Michel Marcus, Mar 27 2018

Extensions

a(31) from Jon E. Schoenfield, Mar 27 2018

a(32)-a(34) from Robert Price, Apr 03 2018

a(35)-a(36) from Robert Price, Jun 01 2018