A317840 Difference between Stern's Diatomic sequence (A002487) and its Möbius transform (A317839).

0, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 3, 4, 1, 1, 4, 1, 3, 4, 5, 1, 2, 3, 5, 4, 3, 1, 4, 1, 1, 6, 5, 5, 4, 1, 7, 6, 3, 1, 8, 1, 5, 6, 7, 1, 2, 3, 7, 6, 5, 1, 8, 7, 3, 8, 7, 1, 4, 1, 5, 10, 1, 7, 6, 1, 5, 8, 9, 1, 4, 1, 11, 8, 7, 7, 10, 1, 3, 8, 11, 1, 8, 7, 13, 8, 5, 1, 12, 7, 7, 6, 9, 9, 2, 1, 9, 8, 7, 1, 12, 1, 5, 14

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to Stern's sequences

Formula

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A002487(d).

a(n) = A002487(n) - A317839(n).

Prog

(PARI)
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A317840(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A002487(d));

Crossrefs

Cf. A002487, A008683, A317837, A317838, A317839, A317841.

Sequence in context: A177219 A277700 A140191 * A048207 A359164 A105810

Adjacent sequences: A317837 A317838 A317839 * A317841 A317842 A317843

Keyword

nonn

Author

Antti Karttunen, Aug 09 2018

Status

approved