OFFSET
0,3
COMMENTS
Like in A324338, a few terms preceding each position n = 2^k seem to be a batch of nearby Fibonacci numbers in some order.
LINKS
FORMULA
From Yosu Yurramendi, Oct 22 2019: (Start)
a(2^m+ k) = A324338(2^m+2^(m-1)+k), m > 0, 0 <= k < 2^(m-1)
a(2^m+2^(m-1)+k) = A324338(2^m+ k), m > 0, 0 <= k < 2^(m-1). (End)
From Yosu Yurramendi, Nov 28 2019: (Start)
a(2^(m+1)+k) - a(2^m+k) = A324338(k), m >= 0, 0 <= k < 2^m.
A071585(k)), m >= 0, 0 <= k < 2^(m-1).
From Yosu Yurramendi, Nov 29 2019: (Start)
For n > 0:
MATHEMATICA
Block[{f}, f[m_] := Module[{a = 1, b = 0, n = m}, While[n > 0, If[OddQ[n], b = a + b, a = a + b]; n = Floor[n/2]]; b]; Array[f@ Fold[BitXor, #, Quotient[#, 2^Range[BitLength[#] - 1]]] &, 106, 0]] (* Michael De Vlieger, Dec 14 2019, after Jean-François Alcover at A002487 and Jan Mangaldan at A006068 *)
PROG
(PARI)
A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); };
(R)
maxlevel <- 6 # by choice
#
for(i in 1:2^maxlevel) {
b[2*i ] <- b[i]
b[2*i+1] <- 1 - b[i]
#
# Yosu Yurramendi, Oct 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 23 2019
STATUS
approved