

A001771


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


17



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

1,2


COMMENTS

n is always of the form 4*k + 1
If n is in the sequence and m=2^(n+2)*3*(7*2^n1) 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, Birkhauser, Boston, 1985, Chap. 4, see pp. 381384.
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).
H. C. Williams and C. R. Zarnke, Math. Comp., 22 (1968), 420422.


LINKS

Table of n, a(n) for n=1..21.
Wilfrid Keller, List of primes k.2^n  1 for k < 300
Index entries for sequences of n such that k*2^n1 (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^n1), v=concat(v, n), )); v


CROSSREFS

Cf. A050523, A003307, A002235, A046865, A079906, A046866, A005541, A056725, A046867, A079907.
Cf. A032353, 7*2^n+1 is prime.
Sequence in context: A273762 A273851 A097538 * A288448 A022341 A255651
Adjacent sequences: A001768 A001769 A001770 * A001772 A001773 A001774


KEYWORD

hard,nonn


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



