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A087810 First differences of A029931. 1
1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -9, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -14, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0, 1, 1, 1, -5, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Multiplicative with a(2^e) = 1 - A000217(e-1), a(p^e) = 1 otherwise. - Mitch Harris, May 17 2005

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16385

FORMULA

a(4n) = 1 - T(v_2(n)), else a(n) = 1, where T = A000217 (triangular numbers) and v_2 = A007814 (exponent of 2 in factorization of n).

G.f.: Sum_{k>=0} (k+1)t/(1+t), where t=x^2^k.

MATHEMATICA

Differences[ Table[ (bits = IntegerDigits[n, 2]) . Reverse[ Range[ Length[bits]]], {n, 0, 92}]] (* Jean-Fran├žois Alcover, Sep 03 2012 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%2==0, if(n%4, 1, 1-valuation(n, 2)*(valuation(n, 2)-1)/2), 1))

(PARI) a(n)=polcoeff(sum(k=0, floor(log(n)/log(2)), (k+1)*x^2^k/(1+x^2^k)) + O(x^(n+1)), n)

(Scheme)

(define (A087810 n) (- (A029931 n) (A029931 (- n 1))))

(define (A029931 n) (let loop ((n n) (i 1) (s 0)) (cond ((zero? n) s) ((odd? n) (loop (/ (- n 1) 2) (+ 1 i) (+ s i))) (else (loop (/ n 2) (+ 1 i) s)))))

;; Antti Karttunen, Nov 18 2017

CROSSREFS

Cf. A029931.

Sequence in context: A257179 A259042 A240021 * A321755 A052314 A271606

Adjacent sequences:  A087807 A087808 A087809 * A087811 A087812 A087813

KEYWORD

sign,easy,mult

AUTHOR

Ralf Stephan, Oct 16 2003

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)