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.

27, 737, 909, 1845, 1912, 7078, 27412, 90009, 870129, 990099, 6852899, 9090909, 17388261, 70168376, 70787078, 96096078, 96707298, 162533711, 358006673, 737737737, 1050889491, 2238028254, 3281718034, 4249370147, 9009009009, 11819327599, 12178217823, 13851266943, 18768863945

Offset

1,1

Comments

These concatenations are part of the sequence:

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

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

Links

Table of n, a(n) for n=1..29.

Carlos Rivera, Puzzle 1212 A381732, The Prime Puzzles and Problems Connection.

Example

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

Prog

(Python)
def f(n):
    s, out = list(map(int, str(n))), 0
    for i in range(len(s)-1):
        dir = 1 if s[i+1] - s[i] >= 0 else -1
        for j in range(s[i]+dir, s[i+1], dir):
            out = 10*out + j
    return out
def ok(n):
    return (v:=f(n)) and v%n == 0
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Mar 06 2025

Crossrefs

Sequence in context: A046240 A042406 A279652 * A284039 A387824 A159668

Adjacent sequences: A381729 A381730 A381731 * A381733 A381734 A381735

Keyword

nonn,base

Author

Paolo P. Lava, Mar 05 2025

Extensions

a(19)-a(29) from Michael S. Branicky, Mar 07 2025

Status

approved