A357989 - OEIS

%I #9 Oct 25 2022 03:35:10

%S 0,3,6,9,15,24,29,43,58,53,18,68,298,399,71,373,2628,444,768,2304,

%T 6144,2631,441,3072,1604,10684,33348,1212,3908,11452,836,3075,1209,

%U 43264,98304,33351,3513,1607,10681,1675,3001,44476,4676,12288,3516,176128,524868

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

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

%C 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.

%H Rémy Sigrist, <a href="/A357989/b357989.txt">Table of n, a(n) for n = 1..2000</a>

%H Rémy Sigrist, <a href="/A357989/a357989.txt">C++ program</a>

%e For n = 1:

%e - 0 is evil,

%e - so a(1) = 0.

%e For n = 2:

%e - 1 and 2 are odious,

%e - 0 + 3 and 3 are evil,

%e - so a(2) = 3.

%e - For n = 3:

%e - 4 is odious,

%e - 3 + 5 is odious,

%e - 0 + 3 + 6, 3 + 6 and 6 are evil,

%e - so a(3) = 6.

%o (C++) See Links section.

%Y Cf. A000069, A001969, A357579.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Oct 23 2022