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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.
1
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
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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Mar 05 2025
EXTENSIONS
a(19)-a(29) from Michael S. Branicky, Mar 07 2025
STATUS
approved