A377815 Lexicographically earliest infinite sequence of distinct positive integers such that the binary concatenation of its terms yields the same string as the binary concatenation of the binary weights of its terms.

1, 5, 2, 3, 4, 8, 15, 255, 7, 11, 13, 14, 16, 19, 21, 22, 6, 25, 32, 9, 26, 63, 65535, 23, 28, 10, 12, 64, 17, 95, 111, 128, 27, 256, 4294967295, 29, 35, 18, 20, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 24, 70, 73, 512, 30, 33, 31, 39, 18446744073709551615

Offset

1,2

Comments

The sequence makes huge jumps. For example, here are three consecutive terms: a(70) = 88, a(71) = 2^256-1, a(72) = 97.

Runs of 0 bits induce large terms since z consecutive 0 bits becomes a term with weight at least 2^z and the smallest such is 2^(2^z) - 1.

The base-2 analog of A302656. The first b terms of this sequence's base-b analog are 1,2,...,(b-1), followed by (b^2+b-1).

Links

Dominic McCarty, Table of n, a(n) for n = 1..451

Dominic McCarty, Log log scatterplot of (n, a(n)) for 1 < n <= 10000

Dominic McCarty, Table of n, a(n), binary weight of a(n) for n = 1..100000

Example

(a(n)):
1,   5,  2,  3,   4,    8,   15,      255,   7, ...
(a(n)) in binary:
1, 101, 10, 11, 100, 1000, 1111, 11111111, 111, ...
Binary weights of (a(n)):
1,   2,  1,  2,   1,    1,    4,        8,   3, ...
Binary weights of (a(n)) in binary:
1,  10,  1, 10,   1,    1,  100,     1000,  11, ...
The two binary lines are the same when concatenated.

Crossrefs

Cf. A302656

Sequence in context: A307603 A234593 A262429 * A097078 A302715 A237200

Adjacent sequences: A377812 A377813 A377814 * A377816 A377817 A377818

Keyword

nonn,base

Author

Dominic McCarty, Nov 08 2024

Status

approved