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

0,2

Links

Table of n, a(n) for n=0..82.

Formula

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

Example

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.

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

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).

Sequence in context: A167708 A372764 A135332 * A101242 A342615 A033046

Adjacent sequences: A098322 A098323 A098324 * A098326 A098327 A098328

Keyword

easy,nonn,base

Author

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

Status

approved