OFFSET
1,2
COMMENTS
Leading 0's in binary expansions are ignored.
Positive terms are digitally balanced (A031443).
If m belongs to the sequence, then A056539(m) also belongs to the sequence.
If m and n belong to the sequence, then their binary concatenation also belongs to the sequence (assuming the concatenation with 0 is neutral).
EXAMPLE
The first 16 integers, alongside their binary representations and associate polynomials, are:
k bin(k) P(k)
-- ------ --------------
0 0 0
1 1 -X^2
2 10 2*X+1
3 11 -2*X^2-2*X-1
4 100 X^2+6*X+5
5 101 -X^2-2*X-3
6 110 -X^2+2*X+3
7 111 -3*X^2-6*X-5
8 1000 2*X^2+12*X+14
9 1001 -4
10 1010 4*X+6
11 1011 -2*X^2-8*X-12
12 1100 8*X+12
13 1101 -2*X^2-4*X-6
14 1110 -2*X^2+4
15 1111 -4*X^2-12*X-14
We have constant polynomials for k = 0 and k = 9, so a(1) = 0 and a(2) = 9.
PROG
(PARI) is(n) = { my (b=Vecrev(binary(n))); poldegree(p=sum(k=1, #b, ('X+k-1)^2 * (-1)^b[k]))<=0 }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 15 2020
STATUS
approved