OFFSET
1,1
COMMENTS
These 2^n-1 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
2^67-1 = 10106743618^2+3*3891344499^2 = 9845359982^2+3*4108642899^2
MATHEMATICA
Select[Range[2, 200, 2], Length[FindInstance[x^2 + 3*y^2 == 2^# - 1, {x, y}, Integers]] > 0 &] (* G. C. Greubel, Apr 14 2017 *)
PROG
(PARI) for(i=2, 100, a=factorint(2^i-1)~; has=0; for(j=1, #a, if(a[1, j]%3==2&&a[2, j]%2==1, has=1; break)); if(has==0&&i%2==0, print(i" -\t"a[1, ])))
CROSSREFS
KEYWORD
nonn
AUTHOR
V. Raman, Aug 23 2012
EXTENSIONS
a(24)-a(47) from V. Raman, Aug 28 2012
STATUS
approved