A283192 Lexicographically earliest sequence of distinct terms such that the derived sequence s(n)=CarrylessSum{k=1..n}a(k) contains only distinct terms, where CarrylessSum is the analog of summation for carryless addition.

1, 2, 3, 4, 5, 7, 6, 9, 10, 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 19, 22, 21, 23, 28, 24, 25, 26, 29, 30, 27, 31, 32, 33, 35, 34, 36, 38, 37, 41, 40, 39, 42, 44, 52, 45, 43, 46, 47, 54, 48, 51, 55, 56, 49, 67, 62, 50, 53, 61, 58, 57, 63, 64, 71, 59, 66, 65

Offset: 1

Author

Rémy Sigrist, Mar 02 2017

Keywords

• nonn
• base

Comments

This sequence is a permutation of the natural numbers (with inverse A283194 and fixed points A283206):

- for any k>0, 10^(k-1) is the first k-digit number appearing in this sequence, and the corresponding partial carryless sum is also the first k-digit number appearing in A283193,

- all powers of 10 appear in this sequence, in increasing order,

- if a(m)=10^k, and the least value not yet seen in this sequence, say v, is smaller than 10^k, then a(m+1)=v,

- hence each natural number will eventually appear in this sequence.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A283192
• Index entries for sequences related to carryless arithmetic
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A169890, A283193 (Partial carryless sum), A283194 (Inverse), A283206 (Fixed points).