cp's OEIS Frontend

A162555 a(n) = the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.

%I A162555 #18 Mar 08 2018 02:47:09
%S A162555 1,11,18,4,16,6,14,8,12,10,13,7,15,5,17,3,19,2,9,30,101,201,301,401,
%T A162555 26,76,501,453,49,601,170,32,168,34,20,82,264,38,162,40,160,42,158,44,
%U A162555 106,96,154,48,152,50,150,52,148,54,146,56,21,81,242,60,140,62,138,64,136
%N A162555 a(n) = the smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.
%C A162555 A permutation of the positive integers. - _M. F. Hasler_, Mar 05 2018
%H A162555 Alois P. Heinz, <a href="/A162555/b162555.txt">Table of n, a(n) for n = 1..10000</a> (first 3000 terms from Jean-Marc Falcoz)
%H A162555 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A162555 a(3) = 18 because that makes the sum of the first 3 terms 30, containing a substring of "3." 11 would make a sum of 23, but 11 was already used in a(2).
%o A162555 (Python)
%o A162555 A162555_list, A162555_set, s = [], set(), 0
%o A162555 for i in range(1,10001):
%o A162555     j, si = 1, str(i)
%o A162555     while si not in str(s+j) or j in A162555_set:
%o A162555         j += 1
%o A162555     A162555_list.append(j)
%o A162555     A162555_set.add(j)
%o A162555     s += j # _Chai Wah Wu_, Feb 23 2018
%Y A162555 Cf. A160855 for the same concept using strings of binary for the sum and substring.
%Y A162555 See A300062 for a strictly increasing variant.
%K A162555 nonn,base,look
%O A162555 1,2
%A A162555 _Kerry Mitchell_, Jul 06 2009