A330720 a(n) is the number of ways of writing the binary expansion of n as a product (or concatenation) of nonpalindromes.

0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 0, 1, 3, 3, 3, 3, 3, 3, 2, 2, 3, 4, 2, 2, 2, 3, 1, 1, 3, 2, 1, 2, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 0, 1, 4, 4, 4, 3, 5, 5, 3, 3, 4, 4, 4, 4, 5, 5, 2, 2, 5, 4, 4, 4, 0, 4

Offset

0,11

Comments

This sequence is a variant of A215244.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

a(2^k-1) = 0 for any k >= 0.

a(A020988(k+1)) = 2^k for any k >= 0.

Example

For n = 41:
- the binary expansion of 41 is "101001",
- the possible products of nonpalindromes are "101001", "1010"."01", and "10"."10"."01",
- hence a(41) = 3.

Maple

ispali:= proc(L) L = ListTools:-Reverse(L) end proc:
g:= proc(L) option remember; local m;
    add(procname(L[m+1..-1]), m= remove(t -> ispali(L[1..t]), [$1..nops(L)]))
end proc:
g([]):= 1:
seq(g(convert(n, base, 2)), n=0..100); # Robert Israel, Dec 29 2019

Prog

(PARI) a(n) = my (b=binary(n), v=b!=Vecrev(b)); for (s=1, #b, my (z=b[s..#b]); if (z!=Vecrev(z), v+=a(fromdigits(b[1..s-1], 2)))); v

Crossrefs

Cf. A020988, A154809, A215244, A301453.

Sequence in context: A258045 A239302 A256983 * A080234 A136049 A370219

Adjacent sequences: A330717 A330718 A330719 * A330721 A330722 A330723

Keyword

nonn,base,look

Author

Rémy Sigrist, Dec 28 2019

Status

approved