A366068 - OEIS

%I #42 Dec 11 2023 01:27:44

%S 1263907548,1263908457,1275480639,1275480936,1326708549,1326709458,

%T 1327608549,1327609458,1349067258,1349076258,1349085267,1349085276,

%U 1358067249,1358076249,1358094267,1358094276,1362708549,1362709458,1367085249,1367094258,1367208549,1367209458,1367245809,1367249058,1367249085,1367254908,1367258049,1367258094,1427086359,1427095368,1435907268

%N 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.

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

%H Michael S. Branicky, <a href="/A366068/b366068.txt">Table of n, a(n) for n = 1..2778</a>

%e 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.

%o (Python)

%o from itertools import permutations

%o 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

%Y Cf. A236402.

%K base,fini,full,nonn

%O 1,1

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Oct 15 2023