A366068 Numbers having exactly 10 distinct digits arranged in such a way that the sum of any pair of adjacent digits is a substring of the number.

1263907548, 1263908457, 1275480639, 1275480936, 1326708549, 1326709458, 1327608549, 1327609458, 1349067258, 1349076258, 1349085267, 1349085276, 1358067249, 1358076249, 1358094267, 1358094276, 1362708549, 1362709458, 1367085249, 1367094258, 1367208549, 1367209458, 1367245809, 1367249058, 1367249085, 1367254908, 1367258049, 1367258094, 1427086359, 1427095368, 1435907268

Offset

1,1

Comments

There are 2778 numbers with this property and the last one is 9817263540.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..2778

Example

The first term is 1263907548 and we see that the 9 successive sums of two adjacent digits are, from left to right, 1+2 (=3), 2+6 (=8), 6+3 (=9), 3+9 (=12), 9+0 (=9), 0+7 (=7), 7+5 (=12), 5+4 (=9) and 4+8 (=12); the results between brackets are substrings of the first term.

Prog

(Python)
from itertools import permutations
def afull(): return [int(s) for s in ("".join(c) for c in permutations("0123456789") if c[0]!="0") if all(str(sum(map(int, s[i:i+2]))) in s for i in range(len(s)-1))] # Michael S. Branicky, Oct 15 2023

Crossrefs

Cf. A236402.

Sequence in context: A204606 A104966 A100004 * A113641 A186909 A288089

Adjacent sequences: A366065 A366066 A366067 * A366069 A366070 A366071

Keyword

base,fini,full,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Oct 15 2023

Status

approved