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%I #35 Jan 04 2022 21:52:22
%S 3,19,73,223,331,379
%N Prime numbers p such that the repunit number (10^p - 1)/9 can be written in the form a^2 + 3*b^2.
%C These (10^p - 1)/9 numbers have no prime factors of the form 2 (mod 3) to an odd power.
%H Samuel S. Wagstaff, Jr., The Cunningham Project, <a href="http://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 2^n-1, for odd n's < 1200</a>
%e (10^19 - 1)/9 = 360004294^2 + 3*571987185^2.
%o (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, ])))
%Y Cf. A002275, A004023, A215803.
%K nonn
%O 1,1
%A _V. Raman_, Aug 23 2012
%E 3 more terms from _V. Raman_, Aug 28 2012