A189893 Recurrence sequence derived from the digits of the square root of 5 after its decimal point.

0, 4, 10, 65, 173, 22, 96, 15, 48, 78, 13, 201, 487, 594, 2719, 5146, 8719, 11530, 15308, 76411, 76016, 42220, 67129, 45349, 170266, 255576, 457846, 865810, 1131083, 8045547, 7669757

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

a(0) = 0; for i >= 0, a(i+1) = position of first occurrence of a(i) in decimal places of sqrt(5).

Example

sqrt(5) = 2.2360679774997896964091736687...
So for example, with a(0) = 0, a(1) = 4 because the 4th digit after the decimal point is 0; a(2) = 10 because the 10th digit after the decimal point is 4 and so on.

Maple

with(StringTools): Digits:=10000: G:=convert(evalf(sqrt(5)), 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:

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), A098326 for sqrt(2), A120482 for sqrt(3), A098327 for sqrt(e), A098328 for 2^(1/3).

Sequence in context: A203226 A300642 A146304 * A355375 A197939 A207160

Adjacent sequences: A189890 A189891 A189892 * A189894 A189895 A189896

Keyword

base,nonn,more

Author

Nathaniel Johnston, Apr 30 2011

Status

approved