A098325 Recurrence sequence based on positions of digits in decimal places of sqrt(Pi).

0, 9, 10, 75, 39, 218, 78, 61, 45, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

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

Keywords

• easy
• nonn
• base

Examples

			sqrt(Pi)=1.7724538509055...
So for example, a(2)=9 because 9th decimal place of sqrt(Pi) is 0.
a(3)=10 because 10th decimal place of sqrt(Pi) is 9, a(4)=75 because 10 appears at the 75th to 76th decimal places and so on.
This sequence, like the one for Zeta(3) (A098290), repeats after just a few terms once the sequence hits 4 at position 4.
		

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, A098324 for Golden Ratio, phi. A002161 for digits of sqrt(Pi).

Programs

Maple

with(StringTools): Digits:=1000: G:=convert(evalf(sqrt(Pi)),string): a[0]:=0: for n from 1 to 15 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 sqrt(Pi), a(i+1)=p(i).