A379142 Lexicographically earliest sequence of distinct positive integers such that the sum of terms a(1)..a(n) has no digit in common with the sum of digits in the terms a(1)..a(n).

11, 1, 2, 3, 5, 4, 7, 8, 6, 9, 10, 12, 13, 16, 14, 17, 18, 15, 30, 20, 21, 23, 19, 22, 27, 59, 37, 28, 25, 24, 26, 33, 35, 34, 32, 29, 38, 31, 36, 39, 41, 50, 40, 43, 44, 54, 42, 45, 247, 46, 51, 47, 53, 58, 57, 48, 52, 60, 69, 74, 49, 63, 55, 56, 67, 76, 70, 106, 79, 80, 61, 62, 64, 65, 66, 68, 81, 71, 72, 102, 78, 149, 73, 100, 84, 77, 82, 86, 83, 115

Offset

1,1

Comments

The majority of terms are approximately n, but some terms show dramatic jumps in value, e.g. a(499) = 999999212. This is due to the term sum reaching the next order of magnitude which only contains a leading nonzero digit followed by all zero digits, with the digit sum containing neither of these digits. As this is always possible regardless of the length of the sequence it is likely the sequence is infinite in length and contains all positive integers.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..500

Example

a(1) = 11 as the sum of terms up to a(1) is 11 while the sum of digits is 2, and 2 shares no digit with 11.
a(5) = 5 as the sum of terms a(1)..a(5) is 22 while the sum of digits of these terms is 13, and 13 shares no digit with 22.

Crossrefs

Cf. A007953, A000217, A320081.

Sequence in context: A010196 A039617 A229186 * A214676 A010198 A307245

Adjacent sequences: A379138 A379139 A379140 * A379143 A379144 A379146

Keyword

nonn,base,new

Author

Scott R. Shannon, Dec 16 2024

Status

approved