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.

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

Table of n, a(n) for n=1..76.

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

Adjacent sequences: A359111 A359112 A359113 * A359115 A359116 A359117

Keyword

nonn,base

Author

Scott R. Shannon, Dec 16 2022

Status

approved