A215803 Numbers k such that the repunit number (10^k - 1)/9 can be written in the form a^2 + 3*b^2.

1, 3, 9, 19, 27, 57, 73, 81, 171, 219, 223, 243, 331, 379

Offset

1,2

Comments

These numbers have no prime factors congruent to 2 (mod 3) raised to an odd power.

Links

Table of n, a(n) for n=1..14.

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) for(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, A215802.

Sequence in context: A057257 A029464 A029479 * A014869 A018495 A350978

Adjacent sequences: A215800 A215801 A215802 * A215804 A215805 A215806

Keyword

nonn,base

Author

V. Raman, Aug 23 2012

Extensions

a(1)=1 inserted and seven more terms from V. Raman, Aug 28 2012

Status

approved