A292273 For odd n: a(n) = 0, and for even n: a(n) = -mu(n), where mu is Moebius function (A008683).

0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

Offset

1

Comments

Sum of Möbius function values computed for terms of 3x+1 trajectory started at n, but excluding mu(n) itself. See Marc LeBrun's comment in A087003.

Links

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

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

a(n) = (A000035(n)-1) * A008683(n).

a(n) = A087003(n) - A008683(n).

Conjecture: a(n) = Re(A008683(n)*(i^n)). - Mats Granvik, Jul 06 2024

Prog

(PARI)
A292273(n) = if(n%2, 0, -moebius(n)); \\ After the definition.
\\ Implementation following the Collatz-interpretation:
A006370(n) = if(n%2, 3*n+1, n/2); \\ This function from Michael B. Porter, May 29 2010
A087003(n) = { my(s=1); while(n>1, s += moebius(n); n = A006370(n)); (s); };
A292273(n) = (A087003(n)-moebius(n));
\\ Or more directly as:
A292273(n) = { my(s=0); while(n>1, n = A006370(n); s += moebius(n)); (s); };
(Scheme) (define (A292273 n) (* (- (A000035 n) 1) (A008683 n)))

Crossrefs

Cf. A000035, A006370, A008683, A014682, A039956 (positions of nonzero terms), A087003.

Sequence in context: A324539 A324964 A285957 * A379966 A324772 A285949

Adjacent sequences: A292270 A292271 A292272 * A292274 A292275 A292276

Keyword

sign,easy

Author

Antti Karttunen, Sep 14 2017

Status

approved