A215802 Prime numbers p such that the repunit number (10^p - 1)/9 can be written in the form a^2 + 3*b^2.

3, 19, 73, 223, 331, 379

Offset

1,1

Comments

These (10^p - 1)/9 numbers have no prime factors of the form 2 (mod 3) to an odd power.

Links

Table of n, a(n) for n=1..6.

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

Example

(10^19 - 1)/9 = 360004294^2 + 3*571987185^2.

Prog

(PARI) forprime(i=2, 100, a=factorint(10^i-1)/9~; 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. A002275, A004023, A215803.

Sequence in context: A095662 A090698 A350713 * A202041 A245507 A247059

Adjacent sequences: A215799 A215800 A215801 * A215803 A215804 A215805

Keyword

nonn

Author

V. Raman, Aug 23 2012

Extensions

3 more terms from V. Raman, Aug 28 2012

Status

approved