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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.
4
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.
CROSSREFS
Cf. A169890, A283193 (Partial carryless sum), A283194 (Inverse), A283206 (Fixed points).
Sequence in context: A232639 A232638 A023826 * A369282 A266638 A256231
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 02 2017
STATUS
approved