A368347 a(1) = 1; for n > 1, a(n) is the smallest positive integer that has not yet appeared which contains all the distinct digits of the sum of all previous terms a(1)..a(n-1).

1, 10, 11, 2, 24, 48, 69, 156, 123, 4, 84, 235, 67, 348, 128, 103, 134, 1457, 304, 308, 136, 2357, 1069, 178, 3567, 10239, 126, 182, 10247, 137, 13458, 12345, 567, 2458, 2068, 20567, 1378, 45689, 10348, 102347, 203479, 4568, 12456, 234568, 105689, 3089, 20689, 12678, 204589, 1048, 1023459

Offset

1,2

Comments

The sequence is infinite, although it is unknown if all positive numbers eventually appear. In the first 50000 terms the smallest number not to have appeared is 3. In the same range the largest value is a(49134) = 1023548967, with the sum of all previous terms at that point being 553402987165.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Example

a(3) = 11 as the sum of the first two terms is 1 + 10 = 11, which contains the distinct digit 1, and 11 is the smallest unused number to contain 1.
a(4) = 2 as the sum of the first three terms is 1 + 10 + 11 = 22, which contains the distinct digit 2, and 2 is the smallest unused number to contain 2.
a(5) = 24 as the sum of the first four terms is 1 + 10 + 11 + 2 = 24, which contains the distinct digits 2 and 4, and 24 is the smallest unused number to contain 2 and 4.

Crossrefs

Cf. A368181, A362093, A362075, A342383, A342382.

Sequence in context: A101807 A248025 A303501 * A289985 A065517 A235600

Adjacent sequences: A368344 A368345 A368346 * A368348 A368349 A368350

Keyword

nonn,base

Author

Scott R. Shannon, Dec 22 2023

Status

approved