A087157 Satisfies a(1)=1, a(A087158(n+1)) = a(n)+1, with a(m)=1 for all m not found in A087158, where A087158(n+2)=A087158(n+1)+a(n)+1.

1, 2, 1, 3, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 5, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1

Offset

1,2

Comments

Removing all the 1's results in the original sequence with every term incremented by 1.

Links

Table of n, a(n) for n=1..105.

Formula

Records are given by A055588(n): a(A055588(n))=n, where A055588(n)=Fibonacci(2n-2)+1 and Fibonacci(n)=A000045(n).

Example

Initialize all terms to 1. Set a(1)=1, go one term forward,
set a(2)=a(1)+1=2, go 2 terms forward,
set a(4)=a(2)+1=3, go 3 terms forward,
set a(7)=a(3)+1=2, go 2 terms forward,
set a(9)=a(4)+1=4, go 4 terms forward,
set a(13)=a(5)+1=1, etc.
The indices 1,2,4,7,9,13,... form A087158.

Crossrefs

Cf. A087158, A085246.

Sequence in context: A260869 A260870 A282497 * A351094 A351092 A138618

Adjacent sequences: A087154 A087155 A087156 * A087158 A087159 A087160

Keyword

nonn

Author

Paul D. Hanna, Aug 22 2003

Status

approved