A392902 Irregular triangle read by rows: row n lists the distinct prime factors of the generalized Fermat number F_n(6) = 6^(2^n) + 1.

7, 37, 1297, 17, 98801, 353, 1697, 4709377, 2753, 145601, 19854979505843329, 4926056449, 447183309836853377, 28753787197056661026689, 257, 763649, 50307329, 3191106049, 2339340566463317436161, 2983028405608735541756929, 18247770097021321924017185281

Offset

0,1

Comments

F_n(6) is currently known to be prime only for n <= 2.

Links

Table of n, a(n) for n=0..20.

Wilfrid Keller, Prime factors of generalized Fermat numbers F_m(6) and complete factoring status.

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

Wikipedia, Generalized Fermat numbers.

Example

Triangle begins:
     | F_n(6) =   |
   n | A078303(n) | Distinct prime factors of F_n(6)
  --------------------------------------------------------------------------
   0 |    6^1 + 1 | 7;
   1 |    6^2 + 1 | 37;
   2 |    6^4 + 1 | 1297;
   3 |    6^8 + 1 | 17, 98801;
   4 |   6^16 + 1 | 353, 1697, 4709377;
   5 |   6^32 + 1 | 2753, 145601, 19854979505843329;
   6 |   6^64 + 1 | 4926056449, 447183309836853377, 28753787197056661026689;
  ...

Mathematica

A392902row[n_] := FactorInteger[6^2^n + 1][[All, 1]];
Array[A392902row, 7, 0]

Crossrefs

Cf. A078303, A253242.

Cf. A050922 (b=2), A392900 (b=3), A392901 (b=5), A392903 (b=7), A393152 (b=8), A391444 (b=10), A392904 (b=11), A392905 (b=12).

Sequence in context: A155010 A292807 A210620 * A250843 A078303 A127729

Adjacent sequences: A392899 A392900 A392901 * A392903 A392904 A392905

Keyword

nonn,tabf,hard

Author

Paolo Xausa, Jan 27 2026

Status

approved