A001771 Numbers k such that 7*2^k - 1 is prime.

1, 5, 9, 17, 21, 29, 45, 177, 18381, 22529, 24557, 26109, 34857, 41957, 67421, 70209, 169085, 173489, 177977, 363929, 372897

Offset: 1

Author

N. J. A. Sloane

Keywords

• hard
• nonn
• more

Comments

k is always of the form 4*j + 1.

If k is in the sequence and m=2^(k+2)*3*(7*2^k-1) then phi(m)+sigma(m)=3m (m is in the sequence A011251). The proof is easy. - Farideh Firoozbakht, Mar 04 2005

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
• 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. A050523, A003307, A002235, A046865, A079906, A046866, A005541, A056725, A046867, A079907.

Cf. A032353 (7*2^k+1 is prime).

Programs

Mathematica

Do[ If[ PrimeQ[7*2^n - 1], Print[n]], {n, 1, 2500}]

PARI

v=[ ]; for(n=0,2000, if(isprime(7*2^n-1),v=concat(v,n),)); v

Extensions

More terms from Douglas Burke (dburke(AT)nevada.edu).

More terms from Hugo Pfoertner, Jun 23 2004