A098328 Recurrence sequence derived from the digits of the cube root of 2 after its decimal point.

0, 7, 14, 42, 147, 321, 473, 322, 785, 1779, 3039, 1957, 16446, 274134, 374781, 110639, 248175, 385504, 2359264, 5108010, 3822244, 3812946, 9896631

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(1)=0. a(1)=0, p(i)=position of first occurrence of a(i) in decimal places of 2^(1/3), a(i+1)=p(i).

Example

2^(1/3)=1.259921049894873164767210607...
So for example, with a(1)=0, a(2)=7 because the 7th digit after the decimal point is 0; a(3)=14 because the 14th digit after the decimal point is 7 and so on.

Maple

with(StringTools): Digits:=10000: G:=convert(evalf(root(2, 3)), string): a[0]:=0: for n from 1 to 12 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), A098325 for sqrt(Pi), A098326 for sqrt(2), A098327 for sqrt(e). A002580 for digits of 2^(1/3).

Sequence in context: A333594 A067048 A189046 * A062098 A045759 A166637

Adjacent sequences: A098325 A098326 A098327 * A098329 A098330 A098331

Keyword

base,more,nonn

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 14 2004

Extensions

More terms from Ryan Propper, Jul 21 2006

Status

approved