A392902 - OEIS

%I #10 Feb 07 2026 04:20:11

%S 7,37,1297,17,98801,353,1697,4709377,2753,145601,19854979505843329,

%T 4926056449,447183309836853377,28753787197056661026689,257,763649,

%U 50307329,3191106049,2339340566463317436161,2983028405608735541756929,18247770097021321924017185281

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

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

%H Wilfrid Keller, <a href="http://www.prothsearch.com/GFN06.html">Prime factors of generalized Fermat numbers F_m(6) and complete factoring status</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fermat_number#Generalized_Fermat_numbers">Generalized Fermat numbers</a>.

%e Triangle begins:

%e      | F_n(6) =   |

%e    n | A078303(n) | Distinct prime factors of F_n(6)

%e   --------------------------------------------------------------------------

%e    0 |    6^1 + 1 | 7;

%e    1 |    6^2 + 1 | 37;

%e    2 |    6^4 + 1 | 1297;

%e    3 |    6^8 + 1 | 17, 98801;

%e    4 |   6^16 + 1 | 353, 1697, 4709377;

%e    5 |   6^32 + 1 | 2753, 145601, 19854979505843329;

%e    6 |   6^64 + 1 | 4926056449, 447183309836853377, 28753787197056661026689;

%e   ...

%t A392902row[n_] := FactorInteger[6^2^n + 1][[All, 1]];

%t Array[A392902row, 7, 0]

%Y Cf. A078303, A253242.

%Y 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).

%K nonn,tabf,hard

%O 0,1

%A _Paolo Xausa_, Jan 27 2026