A392904 - OEIS

%I #13 Feb 07 2026 04:20:40

%S 2,3,2,61,2,7321,2,17,6304673,2,51329,447600088289,2,193,257,

%T 21283620033217629539178799361,2,316955440822738177,

%U 7032401262704707649518767703756385761576062060673,2,15361,111489577217,574341646346402207998363393,4018529583345312964042058778793458689,2513867991837362316715332574077411130744618580176804609

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

%C No F_n(11) number is prime.

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

%H Wilfrid Keller, <a href="http://www.prothsearch.com/GFN11.html">Prime factors of generalized Fermat numbers F'_m(11) = F_m(11)/2 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(11) =  |

%e    n | A199592(n) | Distinct prime factors of F_n(11)

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

%e    0 |   11^1 + 1 | 2, 3;

%e    1 |   11^2 + 1 | 2, 61;

%e    2 |   11^4 + 1 | 2, 7321;

%e    3 |   11^8 + 1 | 2, 17, 6304673;

%e    4 |  11^16 + 1 | 2, 51329, 447600088289;

%e    5 |  11^32 + 1 | 2, 193, 257, 21283620033217629539178799361;

%e   ...

%t A392904row[n_] := FactorInteger[11^2^n + 1][[All, 1]];

%t Array[A392904row, 7, 0]

%Y Cf. A199592, A253242.

%Y 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).

%K nonn,tabf,hard

%O 0,1

%A _Paolo Xausa_, Jan 27 2026