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 A374725 #20 Jul 21 2024 00:40:54 %S A374725 1,11,121,1331,14641,161051,1771561,19487171,233846052,5846151300 %N A374725 The "multiplicative comma sequence": the lexicographically earliest sequence of positive integers with the property that the sequence formed by the pairs of digits adjacent to the commas between the terms is the same as the sequence of successive ratios between the terms. %C A374725 A more formal definition can be given as follows: a(1) = 1; for n > 1, let x be the least significant digit of a(n-1); then a(n) = a(n-1) * (10*x + y), with y being the most significant digit of a(n). Choose the smallest such y if such a y exists. If no such y exists, the sequence ends. We also restrict y to being a nonzero digit. %C A374725 The sequence is given in its entirety as there is no possible next term after 5846151300. %C A374725 Choosing other values for a(1) yields finite sequences up to a(1) = 10000 as long as a(1) is not of the form 1...0 otherwise the sequence is constant and infinite. For example, if a(1) = 120, then a(2) = 120 because 120 * 01 = 120. %e A374725 Replace each comma in the original sequence by the pair of digits adjacent to the comma; the result is the sequence of first ratios between the terms of the sequence: %e A374725 Sequence: 1, 11, 121, 1331, 14641, 161051, 1771561, 19487171, 233846052, 5846151300 %e A374725 Ratios: 11, 11, 11, 11, 11, 11, 11, 12, 25 %e A374725 For example: a(9) = 233846052 = 12 * 19487171 = 12 * a(8) %t A374725 a[1] = 1; a[n_] := a[n] = For[x = Mod[a[n - 1], 10]; y = 1, y <= 9, y++, an = a[n - 1]*(10*x + y); If[y == IntegerDigits[an][[1]], Return[an]]]; Array[a, 10] %Y A374725 Cf. A121805. %K A374725 nonn,base,fini,full %O A374725 1,2 %A A374725 _Nicholas M. R. Frieler_, Jul 17 2024