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A215801 Prime numbers p such that (2^p + 1)/3 can be written in the form a^2 + 3*b^2. 2
3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 109, 127, 139, 151, 199, 277, 313, 433, 457, 547, 613, 619, 643, 739, 967 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..26.

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

PROG

(PARI) forprime(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, print(i" -\t"a[1, ])))

CROSSREFS

Cf. A000051, A000978, A215800.

Sequence in context: A215907 A007645 A144919 * A215809 A015916 A023203

Adjacent sequences:  A215798 A215799 A215800 * A215802 A215803 A215804

KEYWORD

nonn

AUTHOR

V. Raman, Aug 23 2012

EXTENSIONS

9 more terms from V. Raman, Aug 28 2012

STATUS

approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)