A292032 a(n) is the value k such that A292030(A292031(n), k) = n.

0, 2, 3, 4, 1, 5, 1, 2, 6, 2, 1, 3, 1, 7, 3, 2, 1, 3, 4, 2, 3, 8, 1, 4, 1, 2, 3, 2, 4, 5, 1, 2, 3, 4, 9, 3, 1, 5, 4, 2, 1, 3, 1, 4, 3, 5, 1, 6, 4, 2, 3, 2, 1, 5, 1, 10, 3, 2, 4, 3, 6, 5, 3, 4, 1, 3, 1, 2, 4, 5, 1, 3, 1, 6, 3, 2, 7, 5, 4, 2, 3, 2, 1, 4, 1, 5, 6, 2, 4, 11

Offset: 0

Author

Ely Golden, Sep 08 2017

Keywords

• nonn

Comments

a(n) > 0 for all n > 0.

for n != 1 the value is unique. For n = 1 A292030(A292031(n), 1) = A292030(A292031(1), 2) = 1. a(n) = 2 by convention.

Examples

			a(2)=3 since A292030(A292031(2),3) = A292030(0,3) = 2.
		

Links

• Ely Golden, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A292031, A292030.

Programs

Python

def smallestSeq(n):
  if(n<0): return []
  if(n==0): return [0,0]
  j,r0,r1=0,0,1
  while(r1<=n): r0,r1=r1,r0+r1 ; j+=1
  while(r1>1):
    if(n%r1==r0): return [n//r1,j]
    r1,r0=r0,r1-r0
    j-=1
  return [n-1, j]
for i in range(10001):
  print(str(i)+" "+str(smallestSeq(i)[1]))