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

Author

Scott R. Shannon, Dec 16 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Crossrefs

Cf. A030302, A030303, A359663 (base-10), A027749.