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

Author

Eric Angelini and Giorgos Kalogeropoulos, Oct 15 2023

Keywords

• base
• fini
• full
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A236402.

Programs

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