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A351332 Primes congruent to 1 (mod 3) that divide some Fermat number. 0
274177, 319489, 6700417, 825753601, 1214251009, 6487031809, 646730219521, 6597069766657, 25409026523137, 31065037602817, 46179488366593, 151413703311361, 231292694251438081, 1529992420282859521, 2170072644496392193, 3603109844542291969 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A014752.

REFERENCES

Allan Cunningham, Haupt-exponents of 2, The Quarterly Journal of Pure and Applied Mathematics, Vol. 37 (1906), pp. 122-145.

LINKS

Table of n, a(n) for n=1..16.

Wilfrid Keller, Prime factors k.2^n + 1 of Fermat numbers F_m.

FORMULA

A002476 INTERSECT A023394.

EXAMPLE

a(1) = 503^2 + 27*28^2 = 274177 is a prime factor of 2^(2^6) + 1;

a(2) = 383^2 + 27*80^2 = 319489 is a prime factor of 2^(2^11) + 1;

a(3) = 887^2 + 27*468^2 = 6700417 is a prime factor of 2^(2^5) + 1;

a(4) = 27017^2 + 27*1884^2 = 825753601 is a prime factor of 2^(2^16) + 1;

a(5) = 2561^2 + 27*6688^2 = 1214251009 is a prime factor of 2^(2^15) + 1;

PROG

(PARI) isok(p) = if(p%6==1 && isprime(p), my(z=znorder(Mod(2, p))); z>>valuation(z, 2)==1, return(0));

CROSSREFS

Cf. A002476, A014752, A023394, A204620, A229850, A229853.

Sequence in context: A151650 A128479 A098786 * A235300 A256364 A250509

Adjacent sequences: A351329 A351330 A351331 * A351333 A351334 A351335

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Feb 07 2022

STATUS

approved

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Last modified February 6 11:47 EST 2023. Contains 360104 sequences. (Running on oeis4.)