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 A374913 #19 Feb 13 2025 10:06:25 %S A374913 2,3,6,11,14,15,18,23,26,30,35,39,50,51,54,63,74,75,78,83,86,90,95,98, %T A374913 99,111,114,119,131,134,135,138,146,155,158,174,179,183,186,191,194, %U A374913 198,210,215,219,230,231,239,243,251,254,270,278,299,303,306,315,323,326,330,338,350 %N A374913 Numbers k such that k^(k + 1) == k + 1 (mod 2*k + 1). %H A374913 Michel Marcus, <a href="/A374913/b374913.txt">Table of n, a(n) for n = 1..10000</a> %F A374913 Conjecture (Superseeker): a(n) = A263458(n)/2. - _R. J. Mathar_, Aug 02 2024 %F A374913 The conjectured formula is false. There exist numbers k such that 2*k + 1 is composite and k^(k + 1) == k + 1 (mod 2*k + 1). For example, when k = 1023: 1023^1024 == 1024 (mod 2047) and 2047 = 23*89 is composite. - _Jedrzej Miarecki_, Jan 16 2025 %t A374913 Select[Range[350],Mod[#^(#+1),2#+1]==#+1 &] (* _Stefano Spezia_, Jul 23 2024 *) %o A374913 (Magma) [n: n in [0..350] | n^(n+1) mod (2*n+1) eq n+1]; %o A374913 (PARI) isok(k) = Mod(k, 2*k+1)^(k+1) == k+1; \\ _Michel Marcus_, Feb 05 2025 %Y A374913 Supersequence of A002515 and A374914. %Y A374913 Cf. A374912. %K A374913 nonn %O A374913 1,1 %A A374913 _Juri-Stepan Gerasimov_, Jul 23 2024