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A155877 Sums of three Fermat numbers. 4
9, 11, 13, 15, 23, 25, 27, 37, 39, 51, 263, 265, 267, 277, 279, 291, 517, 519, 531, 771, 65543, 65545, 65547, 65557, 65559, 65571, 65797, 65799, 65811, 66051, 131077, 131079, 131091, 131331, 196611, 4294967303, 4294967305, 4294967307 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Weisstein summarizes: "Ribenboim (1996, pp. 89 and 359-360) defines a generalized Fermat number as a number of the form a^(2^n)+1 with a>2, while Riesel (1994) further generalizes, defining it to be a number of the form a^(2^n) + b^(2^n). Both definitions generalize the usual Fermat numbers F_n = 2^(2^n)+1." In that context, the current sequence extends Riesel's generalization to three terms, not necessarily distinct, all base 2. Primes in this sequence begin 11, 13, 23, 37, 263, 277.

LINKS

Table of n, a(n) for n=1..38.

Eric W. Weisstein, "Generalized Fermat Number"

FORMULA

{(2^(2^a) + 1) + (2^(2^b) + 1) + (2^(2^c) + 1) = {A000215(a) + A000215(b) + A000215(c)}.

EXAMPLE

a(1) = 3 + 3 + 3 = 9. a(2) = 3 + 3 + 5 = 11. a(3) = 3 + 5 + 5 = 13. a(4) = 5 + 5 + 5 = 15. a(5) = 3 + 3 + 17 = 23. a(6) = 3 + 5 + 17 = 25. a(7) = 5 + 5 + 17 = 27. a(8) = 3 + 17 + 17 = 37. a(9) = 5 + 17 + 17 = 39. a(10) = 17 + 17 + 17 = 51. a(11) = 3 + 3 + 257 = 263.

CROSSREFS

Cf. A000215, A019434, A050922, A051179, A059919, A063486, A073617, A078303, A078304, A085866.

Sequence in context: A008558 A123760 A251394 * A214865 A225557 A120177

Adjacent sequences:  A155874 A155875 A155876 * A155878 A155879 A155880

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Jan 29 2009

EXTENSIONS

More terms from R. J. Mathar, Feb 06 2009

STATUS

approved

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Last modified May 27 11:14 EDT 2017. Contains 287204 sequences.