A215801 Prime numbers p such that (2^p + 1)/3 can be written in the form a^2 + 3*b^2.

3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 109, 127, 139, 151, 199, 277, 313, 433, 457, 547, 613, 619, 643, 739, 967

Offset: 1

Author

V. Raman, Aug 23 2012

Keywords

• nonn

Comments

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

Links

• Samuel S. Wagstaff, Jr., The Cunningham Project, Factorizations of 2^n-1, for odd n's < 1200

Crossrefs

Cf. A000051, A000978, A215800.

Programs

PARI

forprime(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

9 more terms from V. Raman, Aug 28 2012