A357989 Lexicographically earliest sequence of distinct numbers such that every sum of consecutive terms is an evil number (A001969).

0, 3, 6, 9, 15, 24, 29, 43, 58, 53, 18, 68, 298, 399, 71, 373, 2628, 444, 768, 2304, 6144, 2631, 441, 3072, 1604, 10684, 33348, 1212, 3908, 11452, 836, 3075, 1209, 43264, 98304, 33351, 3513, 1607, 10681, 1675, 3001, 44476, 4676, 12288, 3516, 176128, 524868

Offset

1,2

Comments

This sequence has similarities with A357579; here we avoid odious numbers, there we avoid perfect powers.

This sequence is well defined as we can always extend the sequence with an evil number whose binary expansion has no 1's in common with all sums of consecutive terms so far.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..2000

Rémy Sigrist, C++ program

Example

For n = 1:
- 0 is evil,
- so a(1) = 0.
For n = 2:
- 1 and 2 are odious,
- 0 + 3 and 3 are evil,
- so a(2) = 3.
- For n = 3:
- 4 is odious,
- 3 + 5 is odious,
- 0 + 3 + 6, 3 + 6 and 6 are evil,
- so a(3) = 6.

Prog

(C++) See Links section.

Crossrefs

Cf. A000069, A001969, A357579.

Sequence in context: A352733 A112773 A363615 * A070885 A002597 A360624

Adjacent sequences: A357986 A357987 A357988 * A357990 A357991 A357992

Keyword

nonn,base

Author

Rémy Sigrist, Oct 23 2022

Status

approved