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A178428 5 followed by the generalized Fermat numbers 6^(2^n)+1 (A078303). 4
5, 7, 37, 1297, 1679617, 2821109907457, 7958661109946400884391937, 63340286662973277706162286946811886609896461828097 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If a(0) = 3, the recursion formula* gives the Fermat numbers (A000215).

With a(0) = 3 instead of 5; a(n) = 2 + product_{i=0..n-1} a(i), n >= 1.

The recurrence equation for generalized Fermat numbers F_n(a) = a^(2^n)+1,

  a >= 2, n >= 0, is F_{n}(a) = (F_{n-1}(a)-1)^2 + 1. - Daniel Forgues, Jun 22 2011

LINKS

Table of n, a(n) for n=0..7.

FORMULA

a(0) = 5; a(n) = 2 + product_{i=0..n-1} a(i), n >= 1.

From Daniel Forgues, Jun 22 2011: (Start)

The motivation for this sequence comes from the recurrence for generalized Fermat numbers 6^(2^n)+1 (A078303)

a(n) = 5*a(n-1)*a(n-2)*...*a(1)*a(0) + 2, n >= 0, where for n = 0, we get 5*(empty product, i.e., 1)+ 2 = 7 = a(0). This implies that the terms are pairwise coprime. (End)

MATHEMATICA

Clear[a, n];

a[0] := 5;

a[n_] := a[n] = Product[a[i], {i, 0, n - 1}] + 2;

Table[a[n], {n, 0, 10}]

CROSSREFS

Cf. A000215, A178427, A178426.

Sequence in context: A322380 A006067 A244260 * A147760 A154148 A242241

Adjacent sequences:  A178425 A178426 A178427 * A178429 A178430 A178431

KEYWORD

nonn

AUTHOR

Roger L. Bagula, May 27 2010

EXTENSIONS

Definition simplified by the Assoc. Eds. of the OEIS - May 28 2010

Edited by Daniel Forgues, Jun 22 2011

STATUS

approved

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Last modified July 11 15:58 EDT 2020. Contains 335626 sequences. (Running on oeis4.)