

A215800


Numbers n such that (2^n+1)/3 can be written in the form a^2+3*b^2.


3



1, 3, 7, 9, 13, 19, 21, 27, 31, 37, 39, 43, 49, 57, 61, 63, 67, 73, 79, 81, 93, 109, 111, 117, 127, 129, 139, 147, 151, 171, 183, 189, 199, 201, 217, 219, 237, 243, 247, 259, 277, 279, 301, 313, 327, 333, 351, 361, 381, 387, 417, 427, 433, 441, 453, 457, 513, 547, 549, 553, 567, 589, 597, 603, 613, 619, 643, 651, 657
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OFFSET

1,2


COMMENTS

These (2^n+1)/3 numbers have no prime factors of the form 2 (mod 3) to an odd power.


LINKS

V. Raman, Table of n, a(n) for n = 1..84
Samuel S. Wagstaff, Jr., The Cunningham Project, Factorizations of 2^n1, for odd n's < 1200.


PROG

(PARI) for(i=2, 100, a=factorint(2^i+1)~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0, print(i" \t"a[1, ])))


CROSSREFS

Cf. A000051, A000978, A215801
Sequence in context: A020498 A200567 A107771 * A103601 A291344 A297002
Adjacent sequences: A215797 A215798 A215799 * A215801 A215802 A215803


KEYWORD

nonn


AUTHOR

V. Raman, Aug 23 2012


EXTENSIONS

Added 5 more terms  V. Raman, Aug 29 2012


STATUS

approved



