

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
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OFFSET

1,1


COMMENTS

Weisstein summarizes: "Ribenboim (1996, pp. 89 and 359360) 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: A123760 A289686 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



