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A215802
Prime numbers p such that the repunit number (10^p - 1)/9 can be written in the form a^2 + 3*b^2.
1
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
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
KEYWORD
nonn
AUTHOR
V. Raman, Aug 23 2012
EXTENSIONS
3 more terms from V. Raman, Aug 28 2012
STATUS
approved