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A122902 First occurrence of exponent n>0 in A122901[k] corresponding to the minimum prime of the form (k^(2^n) + (k+1)^(2^n)) = A122900[k] for k>1. 2
1, 3, 23, 21, 10, 95, 255, 86, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(8) = 86, a(9) = 59. Minimum primes of the form n^(2^m) + (n+1)^(2^m) are listed in A122900[n] = {5, 13, 337, 41, 61, 3697, 113, 10657, 181, 2211377674535255285545615254209921, ...}. The exponents m(n) are listed in A122901[n] = { 1, 1, 2, 1, 1, 2, 1, 2, 1, 5, 0, 1, 2, 1, 0, 2, 1, 0, 1, 0, 4, 1, 3, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 4, 1, 2, 0, 4, 0, 1, 2, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 9, 1, 0, 0, 2, 0, 1, 3, 2, 2, 1, 1, 0, 1, 0, 2, 4, 3, 0, 2, 1, 4, 0, 1, 0, 1, 1, 8, 1, 2, 2, 1, 0, 0, 4, 0, 6, 4, 1, 2, 1, 1, ...}.

a(7) = 255. a(10)-a(13)>1000, a(14)-a(16)>100.

LINKS

Table of n, a(n) for n=1..9.

T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m

Eric Weisstein's World of Mathematics, Generalized Fermat Number

EXAMPLE

A122901[n] begins {1,1,2,1,1,2,1,2,1,5,0,1,2,1,0,2,1,0,1,0,4,1,3,1,...}.

So a(1) = 1, a(2) = 3, a(3) = 23, a(4) = 21, a(5) = 10.

CROSSREFS

Cf. A122900, A122901.

Cf. A080208, A078902, A080134.

Cf. A019434, A078902, A080134, A153504, A152913, A194185. - Jonathan Vos Post, Aug 18 2011

Sequence in context: A130475 A212998 A157819 * A297855 A298090 A298052

Adjacent sequences:  A122899 A122900 A122901 * A122903 A122904 A122905

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Sep 18 2006, Oct 01 2006

STATUS

approved

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Last modified February 25 12:01 EST 2020. Contains 332233 sequences. (Running on oeis4.)