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A286678 Smallest prime of the form (1 + k)^(2^n) + k for some k. 0
5, 17, 257, 65537, 795866110996400884391941, 3402823669209384634633746074317682114560000000000000000000000000000000000000000000000000000000000000039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Generated by n (of a(n)): 1, 1, 1, 1, 5, 39, 73, 271, 16, ...

b(n) = smallest prime of the form (1 + m)^(2^n) + m^(2^n) for some m: 5, 17, 257, 65537, 3512911982806776822251393039617, ...

Generated by n (of b(n)): 1, 1, 1, 1, 8, 95, 31, 85, 59, ...

REFERENCES

Eric Weisstein's World of Mathematics, Fermat Prime.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

a(5) = 795866110996400884391941 because 795866110996400884391941 is prime and equal to (1 + 5)^(2^5) + 5 for k = 5.

CROSSREFS

Cf. A000215, A019434, A070592, A100270, A232720, A263539, A272061, A285929, A286982, A287842.

Sequence in context: A274000 A093428 A274002 * A081479 A318751 A096996

Adjacent sequences:  A286675 A286676 A286677 * A286679 A286680 A286681

KEYWORD

nonn,less

AUTHOR

Juri-Stepan Gerasimov, May 12 2017

STATUS

approved

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Last modified August 25 09:58 EDT 2019. Contains 326324 sequences. (Running on oeis4.)