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

Author

Rémy Sigrist, Oct 23 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..2000
• Rémy Sigrist, C++ program

Crossrefs

Cf. A000069, A001969, A357579.