A392904 Irregular triangle read by rows: row n lists the distinct prime factors of the generalized Fermat number F_n(11) = 11^(2^n) + 1.

2, 3, 2, 61, 2, 7321, 2, 17, 6304673, 2, 51329, 447600088289, 2, 193, 257, 21283620033217629539178799361, 2, 316955440822738177, 7032401262704707649518767703756385761576062060673, 2, 15361, 111489577217, 574341646346402207998363393, 4018529583345312964042058778793458689, 2513867991837362316715332574077411130744618580176804609

Offset

0,1

Comments

No F_n(11) number is prime.

F_n(11)/2 is currently known to be prime only for n = 1 and n = 2.

Links

Table of n, a(n) for n=0..24.

Wilfrid Keller, Prime factors of generalized Fermat numbers F'_m(11) = F_m(11)/2 and complete factoring status.

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

Wikipedia, Generalized Fermat numbers.

Example

Triangle begins:
     | F_n(11) =  |
   n | A199592(n) | Distinct prime factors of F_n(11)
  -------------------------------------------------------------
   0 |   11^1 + 1 | 2, 3;
   1 |   11^2 + 1 | 2, 61;
   2 |   11^4 + 1 | 2, 7321;
   3 |   11^8 + 1 | 2, 17, 6304673;
   4 |  11^16 + 1 | 2, 51329, 447600088289;
   5 |  11^32 + 1 | 2, 193, 257, 21283620033217629539178799361;
  ...

Mathematica

A392904row[n_] := FactorInteger[11^2^n + 1][[All, 1]];
Array[A392904row, 7, 0]

Crossrefs

Cf. A199592, A253242.

Cf. A050922 (b=2), A392900 (b=3), A392901 (b=5), A392902 (b=6), A392903 (b=7), A393152 (b=8), A391444 (b=10), A392905 (b=12).

Sequence in context: A291489 A075121 A075108 * A364139 A265590 A260208

Adjacent sequences: A392901 A392902 A392903 * A392905 A392906 A392907

Keyword

nonn,tabf,hard

Author

Paolo Xausa, Jan 27 2026

Status

approved