A091862 - OEIS

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A091862

a(n) = 1 if the sum of all exponents of the prime-factorization of n has no carries when summed in base 2, or a(n) = 0 if there are any carries.

1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0

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OFFSET

1,1

COMMENTS

Characteristic function for A268375. - Antti Karttunen, Nov 23 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

Index entries for sequences related to binary expansion of n.

FORMULA

If A268374(n) = 0, then a(n) = 1, 0 otherwise. - Antti Karttunen, Nov 23 2017

EXAMPLE

a(12) = 1 because 12 = 2^2 *3^1 and, in base 2, 2 = '10', 1 = '1' and '10' and '1' have their ones in different positions. But a(24) = 0 because 24 = 2^3 *3^1 and in base 2 3 = '11', 1 = '1', which both share a rightmost one.

MATHEMATICA

f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; a[n_] := Boole[UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]]; Array[a, 100] (* Amiram Eldar, Dec 23 2023 *)

PROG

(PARI) a(n) = {my(e = factor(n)[, 2], b = 0); for(i=1, #e, b = bitor(b, e[i])); n == 1 || b == vecsum(e); } \\ Amiram Eldar, Dec 23 2023

CROSSREFS

Cf. A091863, A267116, A268374, A289618.

Cf. A268375 (positions of ones), A268376 (of zeros).

Sequence in context: A373851 A142720 A196308 * A351564 A237048 A344880

Adjacent sequences: A091859 A091860 A091861 * A091863 A091864 A091865

KEYWORD

nonn,base

AUTHOR

Leroy Quet, Mar 13 2004

EXTENSIONS

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004

STATUS

approved