A001772 Numbers k such that 11*2^k - 1 is prime.

2, 26, 50, 54, 126, 134, 246, 354, 362, 950, 1310, 2498, 6926, 11826, 31734, 67850, 74726, 96150, 374114, 696438, 743322, 1044086, 1104606, 1261478

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• nice
• more

References

• H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Wilfrid Keller, List of primes k.2^n - 1 for k < 300
• Kosmaj, Riesel list k<300.
• H. C. Williams and C. R. Zarnke, A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1, Math. Comp., 22 (1968), 420-422.
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A050525.

Cf. A002261 (11*2^k+1 is prime).

Programs

PARI

is(n)=ispseudoprime(11*2^n-1) \\ Charles R Greathouse IV, Feb 20 2017

Python

from sympy import isprime
def aupto(lim): return [k for k in range(1, lim+1) if isprime(11*2**k - 1)]
print(aupto(2500)) # Michael S. Branicky, Feb 26 2021

Extensions

More terms from Hugo Pfoertner, Jun 23 2004

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008