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A359114
a(1) = 1; for n > 1, a(n) is the smallest positive number which has not appeared that shares a factor with the sum of the first n bits of the binary Champernowne string starting from 1.
2
1, 2, 4, 3, 6, 5, 10, 15, 8, 9, 7, 12, 18, 21, 14, 11, 16, 13, 26, 39, 52, 20, 22, 24, 25, 28, 30, 17, 34, 27, 32, 19, 35, 33, 36, 38, 40, 23, 42, 44, 45, 46, 48, 49, 50, 29, 51, 31, 54, 55, 57, 60, 63, 66, 56, 58, 62, 64, 65, 68, 69, 70, 37, 74, 72, 76, 78, 75, 80, 41, 82, 77, 81, 84, 43, 86
OFFSET
1,2
COMMENTS
For the binary Champernowne string starting from 1 see A030302. In the first 100000 terms the fixed points are 1, 2, 12, 24, 25; it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.
LINKS
Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.
EXAMPLE
a(3) = 4 as the sum of the first 3 bits of the binary Champernowne string is 1 + 1 + 0 = 2, and 4 is the smallest unused number that shares a factor with 2.
a(10) = 9 as the sum of the first 10 bits of the binary Champernowne string is 1 + 1 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 0 = 6, and 9 is the smallest unused number that shares a factor with 6.
CROSSREFS
Cf. A030302, A030303, A359663 (base-10), A027749.
Sequence in context: A087559 A193298 A168007 * A328108 A091850 A332450
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Dec 16 2022
STATUS
approved