OFFSET
1,1
COMMENTS
The index sequence (a(n)) of a block-fractal sequence (s(n)) is defined by a(n) = least k > 0 such that (s(k), s(k+1), ..., s(k+n)) = (s(0), s(1), ..., s(n)).
FORMULA
a(n) = 3*A053644(n-1) for n >= 2.
EXAMPLE
A010060 = (0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,,...) = (s(0), s(1), ... ).
(initial block #1) = (0) first repeats at s(3), so that a(1) = 3;
(initial block #2) = (0,1) first repeats at s(3), so that a(2) = 3;
(initial block #3) = (0,1,1) first repeats at s(6), so that a(3) = 6.
MATHEMATICA
seq = Table[Mod[Length[FixedPointList[BitAnd[#, # - 1] &, n]], 2], {n, 0, 400}] (* A010060 *)
seq = StringJoin[Map[ToString, seq]]
u = -1 + Most[Flatten[Rest[Reap[NestWhile[# + 1 &, 1,
Sow[First[Last[StringPosition[seq, StringTake[seq, #], 2]]]] >
1 &]]]]] (* A280510 *) (* Peter J. C. Moses, Jan 05 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 10 2017
STATUS
approved