A103479 Positive integers k for which 1 + 6*2^(k+2) divides the Fermat number 1 + 2^2^k.

38, 2478782

Offset: 1

Author

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

Keywords

• nonn
• bref
• hard
• more

Comments

On Keller's linked page, to find the terms, you run through the tables and find all rows with k = 3 and with n exactly 3 greater than m, then that m belongs to this sequence. - Jeppe Stig Nielsen, Dec 04 2018

Examples

			a(1)=38 because 38 is the smallest positive integer k for which 1 + 6*2^(k+2) divides the Fermat number 1 + 2^2^k.
		

Links

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

Crossrefs

Cf. A103477, A103478.

Programs

Mathematica

aQ[n_] := PowerMod[2, 2^n, 1 + 6*2^(n+2)] == 6*2^(n+2); Select[Range[3000000], aQ] (* Amiram Eldar, Dec 04 2018 *)

PARI

isOK(n) = Mod(2, 1+3*2^(n+3))^(2^n) + 1 == 0 \\ Jeppe Stig Nielsen, Dec 03 2018

Extensions

Sequence name trimmed by Jeppe Stig Nielsen, Dec 03 2018