A097686 a(n+1) = if a(n) is even then a(n)/2 else (a(n) + number of earlier occurrences of a(n)), a(1) = 1.

1, 1, 2, 1, 3, 3, 4, 2, 1, 4, 2, 1, 5, 5, 6, 3, 5, 7, 7, 8, 4, 2, 1, 6, 3, 6, 3, 7, 9, 9, 10, 5, 8, 4, 2, 1, 7, 10, 5, 9, 11, 11, 12, 6, 3, 8, 4, 2, 1, 8, 4, 2, 1, 9, 12, 6, 3, 9, 13, 13, 14, 7, 11, 13, 15, 15, 16, 8, 4, 2, 1, 10, 5, 10, 5, 11, 14, 7, 12, 6, 3, 10, 5, 12, 6, 3, 11, 15, 17, 17, 18, 9, 14

Offset

1,3

Comments

a(A097687(n))=n and a(m)<n for m < A097687(n);

A097688(n) = #{k: a(k)=1, 1<=k<=n}.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

A:= Vector(100):
A[1]:= 1: C[1]:= 1:
for n from 2 to 100 do
  if A[n-1]::even then A[n]:= A[n-1]/2
  else A[n]:= A[n-1] + C[A[n-1]]-1;
  fi;
  if assigned(C[A[n]]) then C[A[n]]:= C[A[n]]+1
  else C[A[n]]:= 1
  fi;
od:
seq(A[i], i=1..100); # Robert Israel, Dec 08 2024

Crossrefs

Cf. A001221.

Sequence in context: A265144 A263275 A308057 * A082666 A363619 A363625

Adjacent sequences: A097683 A097684 A097685 * A097687 A097688 A097689

Keyword

nonn,look

Author

Reinhard Zumkeller, Aug 19 2004

Status

approved