A215800 Numbers k such that (2^k+1)/3 can be written in the form a^2 + 3*b^2.

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

Offset: 1

Author

V. Raman, Aug 23 2012

Keywords

• nonn

Comments

These (2^k+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^n-1, for odd n's < 1200.

Crossrefs

Cf. A000051, A000978, A215801.

Programs

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, ])))

Extensions

5 more terms from V. Raman, Aug 29 2012