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 A381732 #23 Mar 29 2025 19:08:42 %S A381732 27,737,909,1845,1912,7078,27412,90009,870129,990099,6852899,9090909, %T A381732 17388261,70168376,70787078,96096078,96707298,162533711,358006673, %U A381732 737737737,1050889491,2238028254,3281718034,4249370147,9009009009,11819327599,12178217823,13851266943,18768863945 %N A381732 Proceeding from left to right, between any two consecutive digits (d_i, d_i+1) of an integer k, write down apart the lacking consecutive digits, in increasing order if d_i <d_i+1 or decreasing order if d_i>d_i+1. If abs(d_i - d_i+1) = 0 or 1 no digit is added. Sequence lists integers k that divide such resulting numbers. %C A381732 These concatenations are part of the sequence: %C A381732 '737' with itself, if it is not a multiple of 7; %C A381732 '7078' with itself, if it is not a multiple of 3. %H A381732 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_1212.htm">Puzzle 1212 A381732</a>, The Prime Puzzles and Problems Connection. %e A381732 27 is a term since between 2 and 7 we have 3456 and 3456 / 27 = 128; %e A381732 1845 is a term since between 1 and 8 we have 234567, between 8 and 4 765 and between 4 and 5 no digit to be added and 234567765 / 1845 = 127137. %o A381732 (Python) %o A381732 def f(n): %o A381732 s, out = list(map(int, str(n))), 0 %o A381732 for i in range(len(s)-1): %o A381732 dir = 1 if s[i+1] - s[i] >= 0 else -1 %o A381732 for j in range(s[i]+dir, s[i+1], dir): %o A381732 out = 10*out + j %o A381732 return out %o A381732 def ok(n): %o A381732 return (v:=f(n)) and v%n == 0 %o A381732 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Mar 06 2025 %K A381732 nonn,base %O A381732 1,1 %A A381732 _Paolo P. Lava_, Mar 05 2025 %E A381732 a(19)-a(29) from _Michael S. Branicky_, Mar 07 2025