A392905 - OEIS

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A392905

Irregular triangle read by rows: row n lists the distinct prime factors of the generalized Fermat number F_n(12) = 12^(2^n) + 1.

8

13, 5, 29, 89, 233, 17, 97, 260753, 153953, 1200913648289, 769, 44450180997616192602560262634753, 36097, 81281, 69619841, 73389730593973249, 77941952137713139794518937770197249, 257, 5312101574902471551211009858792613701359967851693176348913224262954673066874179441584772343144224572301982521857107589870210046272536321

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

F_n(12) is currently known to be prime only for n = 0.

LINKS

Table of n, a(n) for n=0..18.

Wilfrid Keller, Prime factors of generalized Fermat numbers F_m(12) and complete factoring status.

Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Wikipedia, Generalized Fermat numbers.

EXAMPLE

Triangle begins:

| F_n(12) = |

n | A152585(n) | Distinct prime factors of F_n(12)

--------------------------------------------------------

0 | 12^1 + 1 | 13;

1 | 12^2 + 1 | 5, 29;

2 | 12^4 + 1 | 89, 233;

3 | 12^8 + 1 | 17, 97, 260753;

4 | 12^16 + 1 | 153953, 1200913648289;

5 | 12^32 + 1 | 769, 44450180997616192602560262634753;

...

MATHEMATICA

A392905row[n_] := FactorInteger[12^2^n + 1][[All, 1]];

Array[A392905row, 8, 0]

CROSSREFS

Cf. A152585, A253242.

Cf. A050922 (b=2), A392900 (b=3), A392901 (b=5), A392902 (b=6), A392903 (b=7), A393152 (b=8), A391444 (b=10), A392904 (b=11).

Sequence in context: A166207 A121230 A299959 * A278445 A157799 A240121

Adjacent sequences: A392902 A392903 A392904 * A392906 A392907 A392908

KEYWORD

nonn,tabf,hard

AUTHOR

Paolo Xausa, Jan 28 2026

STATUS

approved