A098326 Recurrence derived from the decimal places of sqrt(2). a(0)=0, a(i+1)=position of first occurrence of a(i) in decimal places of sqrt(2).

0, 13, 5, 7, 11, 186, 239, 336, 1284, 5889, 11708, 70286, 19276, 35435, 22479, 42202, 28785, 107081, 973876, 1187108

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 13 2004

Keywords

• more
• nonn
• base

Examples

			sqrt(2)=1.4142135623730950488...
So for example a(2)=13 because 13th decimal place of sqrt(2) is 0; then a(3)=5 because 13 is found starting at the 5th decimal place; a(4)=7 because 5 is at the 7th decimal place 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, A098324 for Golden Ratio (phi), A098325 for sqrt(Pi), A120482 for sqrt(3), A189893 for sqrt(5). A002193 for digits of sqrt(2).

Programs

Maple

with(StringTools): Digits:=10000: G:=convert(evalf(sqrt(2)),string): a[0]:=0: for n from 1 to 10 do a[n]:=Search(convert(a[n-1],string), G)-2:printf("%d, ",a[n-1]):od: # Nathaniel Johnston, Apr 30 2011

Extensions

a(18)-a(19) from Nathaniel Johnston, Apr 30 2011