A359663 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 terms of the Champernowne string starting from 1.

1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 12, 47, 14, 21, 15, 13, 11, 16, 18, 61, 20, 67, 73, 22, 24, 26, 25, 28, 30, 17, 27, 32, 33, 107, 109, 36, 19, 29, 34, 38, 127, 39, 35, 137, 40, 42, 44, 45, 48, 46, 49, 51, 43, 50, 54, 52, 57, 31, 55, 193, 56, 60, 23, 58, 62, 64, 63, 66, 65, 68, 70, 72, 69, 77, 75, 37

Offset

1,2

Comments

For the Champernowne string starting from 1 see A033307. In the first 100000 terms there are 45 fixed points: 1, 4, 5, 6, 7, ..., 252, 264, 319. It is plausible 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) = 2 as the sum of the first 3 terms of the Champernowne string is 1 + 2 + 3 = 6, and 2 is the smallest unused number that shares a factor with 6.
a(10) = 10 as the sum of the first 10 terms of the Champernowne string is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 1 = 46, and 10 is the smallest unused number that shares a factor with 46.

Crossrefs

Cf. A033307, A065648, A359114 (base-2), A027749.

Sequence in context: A089401 A373952 A035044 * A171086 A333324 A333470

Adjacent sequences: A359660 A359661 A359662 * A359664 A359665 A359666

Keyword

nonn,base

Author

Scott R. Shannon, Jan 10 2023

Status

approved