A098324 Recurrence sequence based on positions of digits in decimal places of phi, the Golden Ratio = (1+sqrt(5))/2.

0, 4, 11, 34, 26, 67, 150, 1485, 2497, 8001, 2773, 16668, 39567, 80705, 15643, 19267, 29310, 223602, 2318795, 9376463, 7972671, 2412975, 3754694, 9560425, 1910435

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 03 2004

Keywords

• more
• nonn
• base

Examples

			phi=1.61803398874989484820...
So for example, a(2)=4 because 4th decimal place of phi is 0.
a(3)=11 because 11th decimal place of phi is 4, a(4)=34 because 11 appears at the 34th to 35th decimal places and so on.
		

Crossrefs

Other recurrence sequences: A097614 for Pi, A098266 for e, A098289 for log(2), A098290 for Zeta(3), A098319 for 1/Pi, A098320 for 1/e, A098321 for gamma, A098322 for G, A098323 for 1/G.

Programs

Maple

with(StringTools): Digits:=100000: G:=convert(evalf((1+sqrt(5))/2),string): a[0]:=0: for n from 1 to 17 do a[n]:=Search(convert(a[n-1],string), G)-2:printf("%d, ",a[n-1]):od: # Nathaniel Johnston, Apr 30 2011

Formula

a(1)=0, p(i)=position of first occurrence of a(i) in decimal places of phi, a(i+1)=p(i).

Extensions

a(17)-a(24) from Nathaniel Johnston, Apr 30 2011