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 A342729 #9 Feb 16 2025 08:34:01
%S A342729 1,3,5,7,9,22,24,26,39,41,43,56,58,60,73,75,77,90,92,94,107,109,111,
%T A342729 136,138,140,153,155,157,170,172,174,199,201,203,216,218,220,233,235,
%U A342729 237,262,264,266,279,281,283,296,298,300,313,315,317,330,332,334,347,349
%N A342729 Self numbers in base i-1: numbers not of the form k + A066323(k).
%C A342729 Equivalently, self numbers in base -4, since A066323(k) is also the sum of the digits of k in base -4.
%C A342729 Analogous to self numbers (A003052) using base i-1 representation (A271472) instead of decimal expansion.
%C A342729 The number of terms not exceeding 10^k, for k=1,2,..., is 5, 20, 155, 1507, 15008, 150007, 1500014, 15000011. Is the asymptotic density of this sequence exactly 3/20?
%D A342729 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.
%H A342729 Amiram Eldar, <a href="/A342729/b342729.txt">Table of n, a(n) for n = 1..10000</a>
%H A342729 Walter Penney, <a href="http://dx.doi.org/10.1145/321264.321274">A "binary" system for complex numbers</a>, Journal of the ACM, Vol. 12, No. 2 (1965), pp. 247-248.
%H A342729 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SelfNumber.html">Self Number</a>.
%H A342729 Wikipedia, <a href="http://en.wikipedia.org/wiki/Self_number">Self number</a>.
%t A342729 s[n_] := Module[{v = {{0, 0, 0, 0}, {0, 0, 0, 1}, {1, 1, 0, 0}, {1, 1, 0, 1}}}, Plus @@ Flatten @ v[[1 + Reverse @ Most[Mod[NestWhileList[(# - Mod[#, 4])/-4 &, n, # != 0 &], 4]]]]]; f[n_] := n + s[n]; m = 1000; Complement[Range[m], Select[Union@Array[f, m], # <= m &]]
%Y A342729 Cf. A007608, A066323, A066321, A271472, A342725, A342726, A342727, A342728.
%Y A342729 Similar sequences: A003052 (decimal), A010061 (binary), A010064 (base 4), A010067 (base 6), A010070 (base 8), A339211 (Zeckendorf), A339212 (dual Zeckendorf), A339213 (base phi), A339214 (factorial base), A339215 (primorial base).
%K A342729 nonn,base
%O A342729 1,2
%A A342729 _Amiram Eldar_, Mar 19 2021