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.

1, 11, 18, 4, 16, 6, 14, 8, 12, 10, 13, 7, 15, 5, 17, 3, 19, 2, 9, 30, 101, 201, 301, 401, 26, 76, 501, 453, 49, 601, 170, 32, 168, 34, 20, 82, 264, 38, 162, 40, 160, 42, 158, 44, 106, 96, 154, 48, 152, 50, 150, 52, 148, 54, 146, 56, 21, 81, 242, 60, 140, 62, 138, 64, 136

Offset: 1

Author

Kerry Mitchell, Jul 06 2009

Keywords

• nonn
• base
• look

Comments

A permutation of the positive integers. - M. F. Hasler, Mar 05 2018

Examples

			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).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 3000 terms from Jean-Marc Falcoz)
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A160855 for the same concept using strings of binary for the sum and substring.

See A300062 for a strictly increasing variant.

Programs

Python

A162555_list, A162555_set, s = [], set(), 0
for i in range(1,10001):
    j, si = 1, str(i)
    while si not in str(s+j) or j in A162555_set:
        j += 1
    A162555_list.append(j)
    A162555_set.add(j)
    s += j # Chai Wah Wu, Feb 23 2018