0,1

Alternatively, list of prime factors of terms of A001317 in order of their first appearance. - Labos E. (labos(AT)ana.sote.hu), Jan 21 2002

Comments from T. D. Noe, Jan 29 2009 (Start): That these two definitions give the same sequence follows from the fact (stated as a formula in A001317) that A001317(n) is the product of Fermat numbers F(i) according to which bits of n are set.

For instance, for n=41, the binary representation of n is 101001, which has bits 0, 3 and 5 set. A001317(n) = 3311419785987 = 3*257*4294967297 = F(0)*F(3)*F(5).

This factorization also explains why the "first 31 numbers give odd-sided constructible polygons". I think Hewgill first noticed this factorization. (End)

M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 2nd. ed., 2001; see p. 3.

J. Bernheiden, Fermat Numbers (Text in German)

R. P. Brent, Factorization of the tenth Fermat number

R. P. Brent, Factorization of the eleventh Fermat number

R. P. Brent, Succint proofs of primality for the factors of some Fermat numbers

R. P. Brent & J. M. Pollard, Factorization of the eighth Fermat number

R. P. Brent et al., Three new factors of Fermat numbers

C. K. Caldwell, The Prime Glossary, Fermat divisor

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

R. Munafo, Notes on Fermat numbers

Eric Weisstein's World of Mathematics, Fermat Number

Triangle begins:

3;

5;

17;

257;

65537;

641, 6700417;

274177, 67280421310721;

59649589127497217, 5704689200685129054721;

1238926361552897, 93461639715357977769163558199606896584051237541638188580280321; ...

A001317(127) = 3.5.17.257.65537.641.6700417.274177.6728042130721, A001317(128) = 59649589127497217.5704689200685129054721. See also A050922. Compare with A053576, where 2 and A000215 appear as prime factors. - Labos E. (labos(AT)ana.sote.hu), Jan 21 2002

Cf. A000215, A019434, A093179.

Cf. A001317, A001316, A003401, A045544, A053576, A050922.

Sequence in context: A125045 A093179 A067387 this_sequence A070592 A000215 A123599

Adjacent sequences: A050919 A050920 A050921 this_sequence A050923 A050924 A050925

nonn,tabf,nice

N. J. A. Sloane (njas(AT)research.att.com), Dec 30 1999

More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2000.

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 31 2009 at the suggestion of T. D. Noe