A330086 Least positive integer k such that A014577(k - 1) != A014577(n + k - 1).

2, 1, 4, 2, 1, 1, 3, 4, 2, 1, 1, 2, 1, 1, 3, 8, 2, 1, 4, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 3, 16, 2, 1, 4, 2, 1, 1, 3, 4, 2, 1, 1, 2, 1, 1, 1, 8, 2, 1, 4, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 3, 32, 2, 1, 4, 2, 1, 1, 3, 4, 2, 1, 1, 2, 1, 1, 3, 8, 2, 1, 4, 2, 1, 1

Offset

1,1

Comments

a(2n) = A006519(n) and a(2n+1) = b(n), where (b(n))_{n >= 0} is a 2-automatic sequence defined by applying the coding tau(01234) = 24131 to the fixed point of the morphism defined by 0 -> 01, 1 -> 23, 2 -> 04, 3 -> 23, 4 -> 24.

Links

Peter Luschny, Table of n, a(n) for n = 1..1000

Maple

with(ListTools): with(numtheory):
J := (n, k) -> jacobi(-1, k) <> jacobi(-1, n+k):
a := n -> SelectFirst(k -> J(n, k), [seq(k, k=1..100000)]):
seq(a(n), n=1..86); # Peter Luschny, Dec 02 2019

Mathematica

Block[{nn = 86, s}, s = Array[Boole[EvenQ[((# + 1)/2^IntegerExponent[# + 1, 2] - 1)/2]] &, 3 nn, 0]; Array[Block[{i = 1}, While[s[[i]] == s[[# + i]], i++]; i] &, nn]] (* Michael De Vlieger, Dec 01 2019 *)

Crossrefs

Cf. A014577, A006519.

Sequence in context: A130544 A214027 A007739 * A290935 A031424 A013942

Adjacent sequences: A330083 A330084 A330085 * A330087 A330088 A330089

Keyword

nonn

Author

Jeffrey Shallit, Dec 01 2019

Status

approved