A215804 Odd numbers k such that 10^k + 1 can be written in the form a^2 + 2*b^2.

1, 5, 7, 13, 19, 25, 29, 31, 35, 43, 53, 61, 65, 67, 71, 95, 125, 145, 155, 175, 179, 215, 239, 263, 265, 269, 293, 305

Offset: 1

Author

V. Raman, Aug 23 2012

Keywords

• nonn

Comments

These 10^k + 1 numbers have no prime factors of the form 5 or 7 (mod 8) to an odd power.

Links

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

Crossrefs

Cf. A000533, A001562, A062397, A215805.

Programs

PARI

for(i=2, 100, a=factorint(10^i+1)~; has=0; for(j=1, #a, if(a[1, j]%8>4&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==1, print(i" -\t"a[1, ])))

Extensions

12 more terms from V. Raman, Aug 28 2012