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

1,2

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).

Sequence in context: A232639 A232638 A023826 * A369282 A266638 A256231

Adjacent sequences: A283189 A283190 A283191 * A283193 A283194 A283195

Keyword

nonn,base

Author

Rémy Sigrist, Mar 02 2017

Status

approved