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 A374911 #26 Nov 04 2024 18:12:33 %S A374911 1,2,3,4,3,7,7,7,3,4,7,7,7,7,7,10,3,7,11,7,5,10,7,7,7,18,7,8,21,7,7,7, %T A374911 3,11,7,18,25,7,7,11,5,7,17,7,10,18,7,7,14,14,21,11,10,7,29,14,7,11,7, %U A374911 7,13,7,7,11,3,17,7,7,10,11,21,7,7,7,7,21,10,32,11,7,5,6,7,7,14,10,7,11,19 %N A374911 a(n) = a(2^n mod n) + a(3^n mod n), with a(0) = 1. %C A374911 Conjectured to contain all positive integers. Here are the indexes where each of the first few positive integers appear: %C A374911 1: 0 %C A374911 2: 1 %C A374911 3: 2, 4, 8, 16, 32, ... (2^k, k > 0) %C A374911 4: 3, 9, ... %C A374911 5: 20, 40, 80, 272, 320, 328, ... %C A374911 6: 81, 66469, 144937, ... %C A374911 7: 5, 6, 7, 10, 11, 12, 13,... (all primes appear except 2 and 3) %C A374911 8: 27, 301, 729, 1099, 2107, 2187, 85085, 1594323, ... %C A374911 Most solutions to a(n) = 5 seem to be divisible by 5 and all of them seem to be even. Why? %C A374911 Are 3 and 9 the only solutions to a(n) = 4? %H A374911 John Tyler Rascoe, <a href="/A374911/b374911.txt">Table of n, a(n) for n = 0..10000</a> %F A374911 a(p) = 7 for primes p except 2 and 3. %F A374911 a(2^n) = 3 for n > 0. %t A374911 a[0]=1; a[n_]:=a[PowerMod[2,n,n]]+a[PowerMod[3,n,n]]; Array[a,89,0] (* _Stefano Spezia_, Jul 23 2024 *) %o A374911 (Python) %o A374911 def a(n): %o A374911 return 1 if n == 0 else a(pow(2, n, n)) + a(pow(3, n, n)) %o A374911 (PARI) a(n) = if (n==0, 1, a(lift(Mod(2,n)^n)) + a(lift(Mod(3,n)^n))); \\ _Michel Marcus_, Jul 25 2024 %Y A374911 Cf. A000079, A015910, A066601. %K A374911 nonn,easy %O A374911 0,2 %A A374911 _Bryle Morga_, Jul 23 2024