A381732 - OEIS

%I #23 Mar 29 2025 19:08:42

%S 27,737,909,1845,1912,7078,27412,90009,870129,990099,6852899,9090909,

%T 17388261,70168376,70787078,96096078,96707298,162533711,358006673,

%U 737737737,1050889491,2238028254,3281718034,4249370147,9009009009,11819327599,12178217823,13851266943,18768863945

%N 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 These concatenations are part of the sequence:

%C  '737' with itself, if it is not a multiple of 7;

%C  '7078' with itself, if it is not a multiple of 3.

%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_1212.htm">Puzzle 1212 A381732</a>, The Prime Puzzles and Problems Connection.

%e 27 is a term since between 2 and 7 we have 3456 and 3456 / 27 = 128;

%e 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 (Python)

%o def f(n):

%o     s, out = list(map(int, str(n))), 0

%o     for i in range(len(s)-1):

%o         dir = 1 if s[i+1] - s[i] >= 0 else -1

%o         for j in range(s[i]+dir, s[i+1], dir):

%o             out = 10*out + j

%o     return out

%o def ok(n):

%o     return (v:=f(n)) and v%n == 0

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Mar 06 2025

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Mar 05 2025

%E a(19)-a(29) from _Michael S. Branicky_, Mar 07 2025