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A001269 Table T(n,k) in which n-th row lists prime factors of 2^n + 1 (n >= 0), with repetition. 5
2, 3, 5, 3, 3, 17, 3, 11, 5, 13, 3, 43, 257, 3, 3, 3, 19, 5, 5, 41, 3, 683, 17, 241, 3, 2731, 5, 29, 113, 3, 3, 11, 331, 65537, 3, 43691, 5, 13, 37, 109, 3, 174763, 17, 61681, 3, 3, 43, 5419, 5, 397, 2113, 3, 2796203, 97, 257, 673, 3, 11, 251, 4051 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Rows have irregular lengths.
The length of row n is A054992(n).
REFERENCES
J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
LINKS
Max Alekseyev, Rows n = 0..1122, flattened (rows 0..500 from T. D. Noe)
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
S. S. Wagstaff, Jr., The Cunningham Project
EXAMPLE
Triangle begins:
2;
3;
5;
3,3,17;
3,11;
5,13;
3,43;
257;
...
MATHEMATICA
repeat[{p_, e_}] := Table[p, {e}]; row[n_] := repeat /@ FactorInteger[2^n + 1] // Flatten; Table[row[n], {n, 0, 25}] // Flatten (* Jean-François Alcover, Jul 13 2012 *)
PROG
(PARI) apply( A001269_row(n)=concat(apply(f->vector(f[2], i, f[1]), Col(factor(2^n+1))~)), [0..19]) \\ M. F. Hasler, Nov 19 2018
CROSSREFS
Cf. A060444 (factors w/o repetition), A054992 (row lengths).
Sequence in context: A321882 A281158 A100742 * A201769 A077276 A073684
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved

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Last modified April 21 19:15 EDT 2024. Contains 371881 sequences. (Running on oeis4.)