A292031 a(n) is the smallest value m such that n appears in row m of A292030.

0, 0, 0, 0, 3, 0, 5, 3, 0, 4, 9, 3, 11, 0, 4, 7, 15, 5, 3, 9, 6, 0, 21, 4, 23, 12, 8, 13, 5, 3, 29, 15, 10, 6, 0, 11, 35, 4, 7, 19, 39, 13, 41, 8, 14, 5, 45, 3, 9, 24, 16, 25, 51, 6, 53, 0, 18, 28, 11, 19, 4, 7, 20, 12, 63, 21, 65, 33, 13, 8, 69, 23, 71, 5, 24, 37, 3, 9, 15, 39, 26

Offset: 0

Author

Ely Golden, Sep 08 2017

Keywords

• nonn

Comments

a(n) = 0 if and only if n is a member of A000045.

a(n) is never 1 nor 2 since row 1 and 2 are equal to row 0 with a shift. - Michel Marcus, Sep 27 2017, amended by M. F. Hasler, Feb 26 2018

Examples

			a(3)=0 since A292030(0,5) = 3.
a(7)=3 since A292030(3,2) = 7.
		

Links

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

Crossrefs

Cf. 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)[0]))