This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364699 #11 Jun 02 2025 15:27:01 %S A364699 1,4,9,16,21,40,45,52,57,64,69,76,100,112,117,129,136,141,177,184,201, %T A364699 220,225,232,244,261,285,297,304,309,316,321,364,376,381,405,412,429, %U A364699 441,460,465,477,484,489,496,520,525,532,544,549,597,609,616,640,645,652,664,681,700,705,712,717 %N A364699 Numbers k such that 1 + 2^k + 3^k is divisible by 2*k-1. %C A364699 k is a term if 2^(k-1) == 1 and 3^(k-1) == -1 (mod 2*k-1). This is true if 2*k-1 is in A290402. Terms such that 2*k-1 is not in A290402 include 1, 2586801, 3393664, and 7989004. Are there any terms such that 2^(k-1) and 3^(k-1) are not == 1 and -1 (respectively) mod 2*k-1? %H A364699 Robert Israel, <a href="/A364699/b364699.txt">Table of n, a(n) for n = 1..10000</a> %e A364699 a(3) = 9 is a term because 1 + 2^9 + 3^9 = 20196 = 1188 * 17 is divisible by 2*9-1 = 17. %p A364699 select(k -> 1 + 2 &^ k + 3 &^ k mod (2*k-1) = 0, [$1..1000]); %t A364699 Select[Range[720], Divisible[PowerMod[3, #, 2*# - 1] + PowerMod[2, #, 2*# - 1] + 1, 2*# - 1] &] (* _Amiram Eldar_, Aug 03 2023 *) %Y A364699 Cf. A001550, A290402, A364683. %K A364699 nonn %O A364699 1,2 %A A364699 _Robert Israel_, Aug 02 2023