A357433 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that the binary string of a(n) plus the sum of all previous terms appears in the binary string concatenation of a(1)..a(n-1).

1, 2, 3, 5, 12, 4, 9, 10, 11, 16, 14, 6, 7, 18, 17, 13, 15, 8, 20, 22, 24, 33, 26, 31, 21, 19, 25, 35, 30, 28, 56, 34, 36, 43, 32, 42, 37, 23, 29, 38, 27, 58, 45, 60, 46, 52, 44, 50, 72, 53, 54, 41, 65, 47, 40, 48, 66, 51, 64, 49, 57, 61, 67, 93, 77, 59, 74, 100, 75, 69, 91, 73, 83, 71, 81, 39, 82

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 20000 terms there are twenty-five fixed points starting 3, 37, 84, 99, 103, 166.

Links

Table of n, a(n) for n=1..77.

Scott R. Shannon, Image of the first 20000 terms. The green line is a(n) = n.

Example

a(5) = 12 as a(1) + a(2) + a(3) + a(4) + 12 = 1 + 2 + 3 + 5 + 12 = 23 = 10111_2, and "10111" appears in the string concatenation of the binary values of a(1)..a(4) = "11011101".

Crossrefs

Cf. A357432 (base 10), A000027, A007088, A007908, A000217, A341766, A337227.

Sequence in context: A127814 A162253 A321855 * A112978 A187129 A341700

Adjacent sequences: A357430 A357431 A357432 * A357434 A357435 A357436

Keyword

nonn,base

Author

Scott R. Shannon, Sep 28 2022

Status

approved