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 A328567 #11 Oct 21 2019 14:45:01 %S A328567 3,6,21,12,75,42,105,24,279,150,341,84,403,210,465,48,1071,558,1197, %T A328567 300,1323,682,1449,168,1575,806,1701,420,1827,930,1953,96,4191,2142, %U A328567 4445,1116,4699,2394,4953,600,5207,2646,5461,1364,5715,2898,5969,336,6223,3150 %N A328567 a(n) is the smallest positive integer divisible by n such that it is possible to strike out a digit from its binary expansion (apart from trailing zeros) so that the resulting number is nonzero and divisible by n. %C A328567 This sequence is a binary variant of A309631. %C A328567 This kind of sequence is well defined for any fixed base b > 1: for any n > 0: consider the concatenation in base b, say m, of n, "0", and n; m is a multiple of n, and removing the central "0" (which is not a trailing zero), gives another multiple of n. %H A328567 Rémy Sigrist, <a href="/A328567/b328567.txt">Table of n, a(n) for n = 1..8192</a> %H A328567 Rémy Sigrist, <a href="/A328567/a328567.gp.txt">PARI program for A328567</a> %F A328567 Apparently, a(n)/n = 2^(1+A070940(n)) - 1. %e A328567 For n = 3: %e A328567 - the first multiples of 3 are (in decimal and in binary), alongside the possible values resulting from striking out a non-trailing zero: %e A328567 3*k bin(3*k) striked (binary) %e A328567 --- -------- ---------------- %e A328567 3 11 1 %e A328567 6 110 10 %e A328567 9 1001 1, 100, 101 %e A328567 12 1100 100 %e A328567 15 1111 111 %e A328567 18 10010 10, 1000, 1010 %e A328567 21 10101 101, 1001, 1010, 1011, 1101 %e A328567 - 21 is the least appropriate multiple, %e A328567 - so a(3) = 21. %o A328567 (PARI) See Links section. %Y A328567 Cf. A070940, A309631. %K A328567 nonn,base %O A328567 1,1 %A A328567 _Rémy Sigrist_, Oct 20 2019