A225855 Difference between the number of nonnegative evil and odious multiples of n less than 2^n.

-1, -1, 3, -1, 5, 9, -7, -1, 27, 25, 11, 162, 13, 49, 521, -1, 697, 2196, 19, 625, 8435, 121, -23, 59049, 3120, 169, 177147, 2401, 29, 982635, -237367, -1, 3958307, 781745, 121691, 28697814, 37, 361, 89405461, 1953125

Offset: 1

Author

Ralf Stephan, Aug 31 2013

Keywords

• sign
• hard
• more

Comments

It appears that for n = 2^i*p, i>0, p prime, a(n) = p^(2^i) or a multiple of it.

For which n is a(n) negative?

For prime n and related conjectures, see A133954.

Crossrefs

Cf. A000069, A001969, A133954.

Programs

PARI

a(n)=sum(i=0,floor(2^n/n),subst(Pol(binary(i*n)),x,1)%2==0)-sum(i=0,floor(2^n/n),subst(Pol(binary(i*n)),x,1)%2)

Extensions

a(31)-a(40) from Amiram Eldar, Apr 23 2022