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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS This sequence is a variant of A215244. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 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 A225192 Adjacent sequences: A330717 A330718 A330719 * A330721 A330722 A330723 KEYWORD nonn,base,look AUTHOR Rémy Sigrist, Dec 28 2019 STATUS approved

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Last modified February 8 12:47 EST 2023. Contains 360138 sequences. (Running on oeis4.)