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 A230638 #37 Sep 05 2024 15:37:03
%S A230638 0,17,16385,16777234
%N A230638 Smallest number m such that u + (sum of base-4 digits of u) = m has exactly n solutions.
%C A230638 Indices of records in A230632: a(n) is the index of the first n in A230632.
%C A230638 The terms are a(1)=0, a(2)=4^2+1, a(3)=4^7+1, a(4)=4^12+17+1, a(5)=4^5368+17+1, a(6)=4^10924+16385+1, a(7)=4^5597880+16385+20. Note that a(7) breaks the pattern of the first six terms.
%C A230638 a(8) = 4^16777229 + 4^12 + 19.
%C A230638 For the leading power of 4 see A230637.
%H A230638 Max Alekseyev, <a href="/A230638/a230638.txt">Table of expressions for a(n), for n=1..100</a>
%H A230638 Max A. Alekseyev and N. J. A. Sloane, <a href="https://arxiv.org/abs/2112.14365">On Kaprekar's Junction Numbers</a>, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
%H A230638 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A230638 n=2: the two solutions to u+(base-4 digit-sum of u) = 17 are 13 and 16.
%e A230638 n=3: the three solutions to u+(base-4 digit-sum of u) = 4^7+1 are 4^7, 4^7-15, 4^7-18.
%e A230638 n=4: the four solutions to u+(base-4 digit-sum of u) = 4^12+17+1 are 4^12+{16, 13, -14, -17}.
%Y A230638 Cf. A230637.
%Y A230638 Related base-4 sequences: A053737, A230631, A230632, A010064, A230633, A230634, A230635, A230636, A230637, A230638, A010065 (trajectory of 1)
%Y A230638 Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.
%K A230638 nonn,base
%O A230638 1,2
%A A230638 _N. J. A. Sloane_, Oct 31 2013
%E A230638 a(8) from _Max Alekseyev_, Oct 31 2013