A001771 Numbers k such that 7*2^k - 1 is prime. (Formerly M3784 N1541)

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

Offset

1,2

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

Table of n, a(n) for n=1..21.

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

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A273762 A273851 A097538 * A288448 A022341 A255651

Adjacent sequences: A001768 A001769 A001770 * A001772 A001773 A001774

Keyword

hard,nonn,more

Author

N. J. A. Sloane

Extensions

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

More terms from Hugo Pfoertner, Jun 23 2004

Status

approved