A103478 Positive integers k for which 1 + 5*2^(k+2) divides the Fermat number 1 + 2^2^k.

5, 23, 73, 125, 1945, 23471

Offset

1,1

Comments

On Keller's linked page, to find the terms, you run through the tables and find all rows with k = 5 and with n exactly 2 greater than m, then that m belongs to this sequence. - Jeppe Stig Nielsen, Dec 04 2018

Links

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

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

Example

a(1)=5 because 5 is the smallest positive integer k for which 1 + 5*2^(k+2) divides the Fermat number 1 + 2^2^k.

Mathematica

Select[Range[1, 2000], Mod[1 + PowerMod[2, 2^#, 1 + 5*2^(# + 2)], 1 + 5*2^(# + 2)] == 0 &] (* Julien Kluge, Jul 08 2016 *)

Prog

(PARI) isok(n) = Mod(2, 1+5*2^(n+2))^(2^n) + 1 == 0; \\ Michel Marcus, Apr 29 2016

Crossrefs

Cf. A000215, A083575, A103477, A103479.

Sequence in context: A230497 A138905 A125955 * A327976 A121868 A111584

Adjacent sequences: A103475 A103476 A103477 * A103479 A103480 A103481

Keyword

nonn,more,hard

Author

Serhat Sevki Dincer (mesti_mudam(AT)yahoo.com), Feb 07 2005

Status

approved