A215891 Numbers k such that P = 2^k - 1 - Sum_{primes p<k} 2^(p-1) is prime.

2, 3, 6, 10, 14, 31, 38, 40, 92, 94, 224, 265, 305, 347, 375, 442, 542, 1326, 2131, 2749, 3837, 5461, 10194, 23128, 24414, 24960, 25536, 38828, 48819

Offset

1,1

Comments

These primes P have k binary digits, all equal to 1 except for digits 0 at prime positions (reading from the right, with 2^0 being position 1, 2^1 being position 2, etc.).

Sequence A215888 is a variant of the same idea, where positions are counted from 0 on.

Links

Table of n, a(n) for n=1..29.

G. L. Honaker Jr. and Chris Caldwell (Eds.), Prime curio for 5461.

Example

a(3) = 6 is in the sequence because 2^6 - 1 - 2^(2 - 1) - 2^(3 - 1) - 2^(5 - 1) = 41 is prime; 41 = 101001_2 has 6 binary digits which are zero in the 2nd, 3rd and 5th position (from the right), and 1's in the other positions.

Mathematica

Select[Range[500], PrimeQ[2^# - 1 - Sum[2^(Prime[i] - 1), {i, PrimePi[# - 1]}]] &] (* Alonso del Arte, Aug 25 2012 *)

Prog

(PARI) is_A215891(N)=ispseudoprime(2^N-1-sum(n=1, primepi(N-1), 2^(prime(n)-1)))

Crossrefs

Sequence in context: A337611 A325724 A111467 * A254033 A356314 A102366

Adjacent sequences: A215888 A215889 A215890 * A215892 A215893 A215894

Keyword

nonn,nice,hard,more

Author

M. F. Hasler, Aug 25 2012

Extensions

a(23) from Jon E. Schoenfield, Jul 08 2015

a(24)-a(27) from Jon E. Schoenfield, Feb 15 2021

a(28)-a(29) from Amiram Eldar, Feb 20 2021

Status

approved