A319687 - OEIS

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A319687

a(n) = A318509(n) - A002487(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 6, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, -6, 0, -4, 0, 0, 0, -4, 0, -6, 0, 10, 0, 0, 0, 4, 2, 0, -2, 0, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,15

COMMENTS

All terms seem to be even. See the conjecture given in A261179.

LINKS

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

Index entries for sequences related to Stern's sequences

FORMULA

a(n) = A318509(n) - A002487(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

A318509(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = A002487(f[i, 1])); factorback(f); };

A319687(n) = (A318509(n) - A002487(n));

(Python)

from math import prod

from functools import reduce

from sympy import factorint

def A319687(n): return prod(sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(p)[-1:2:-1], (1, 0)))**e for p, e in factorint(n).items())-sum(reduce(lambda x, y:(x[0], x[0]+x[1]) if int(y) else (x[0]+x[1], x[1]), bin(n)[-1:2:-1], (1, 0))) # Chai Wah Wu, May 18 2023

CROSSREFS

Cf. A002487, A261179, A317837, A318509, A323365.

Sequence in context: A350139 A293814 A045837 * A374217 A126825 A045833

Adjacent sequences: A319684 A319685 A319686 * A319688 A319689 A319690

KEYWORD

sign,look

AUTHOR

Antti Karttunen, Oct 02 2018

STATUS

approved