A357482 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1).

0, 1, 2, 3, 7, 4, 5, 63, 8, 6, 9, 16, 127, 11, 10, 12, 13, 14, 19, 511, 1023, 15, 21, 17, 31, 18, 20, 22, 24, 25, 33, 23, 27, 26, 28, 35, 37, 38, 41, 1535, 29, 30, 32, 34, 47, 36, 40, 55, 39, 43, 42, 45, 255, 46, 51, 383, 48, 44, 4095, 64, 447, 65, 95, 53, 191, 767, 1791, 59, 49, 54, 57, 50, 52

Offset

0,3

Comments

The sequence contains large jumps in value due to some terms having to be 1 less than a power of 2 to contain sufficient 1's in their binary value to meet the term selection criteria. For example a(386) = 512, a(387) = 68719476735. See the examples below.

Links

Table of n, a(n) for n=0..72.

Example

a(7) = 63 as 63 = 111111_2 which contains six 1's, the concatenation of the binary values of a(0)..a(6) is "011011111100101" which contains ten 1's, and 6 + 10 = 16 = 10000_2 which does not appear in the concatenated binary string of previous terms. All smaller unused numbers less than 63 have one to five 1's in their binary values leading to sums of 11, 12, 13, 14 or 15, but the binary values of these five sums all appear in the concatenated binary string of previous terms.

Crossrefs

Cf. A357082, A357449, A355611, A007088, A030302, A118248.

Sequence in context: A195795 A143528 A118810 * A026259 A168087 A168085

Adjacent sequences: A357479 A357480 A357481 * A357483 A357484 A357485

Keyword

nonn,base

Author

Scott R. Shannon, Sep 30 2022

Status

approved