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A330720
a(n) is the number of ways of writing the binary expansion of n as a product (or concatenation) of nonpalindromes.
1
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.
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
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Dec 28 2019
STATUS
approved