cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A098290 Recurrence sequence based on positions of digits in decimal places of Zeta(3) (Apery's constant).

Original entry on oeis.org

0, 2, 1, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10
Offset: 0

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 02 2004

Keywords

Comments

This recurrence sequence starts to repeat quite quickly because 1 appears at the 10th digit of Zeta(3), which is also where 159 starts.
Can the transcendental numbers such that recurrence relations of this kind eventually repeat be characterized? - Nathaniel Johnston, Apr 30 2011

Examples

			Zeta(3) = 1.2020569031595942853997...
a(0)=0, a(1)=2 because 2nd decimal = 0, a(2)=1 because first digit = 2, etc.

Crossrefs

Cf. A002117 for digits of Zeta(3). 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), A189893 for sqrt(5), A098327 for sqrt(e), A098328 for 2^(1/3).

Programs

  • Maple
    with(StringTools): Digits:=400: G:=convert(evalf(Zeta(3)-1), string): a[0]:=0: for n from 1 to 50 do a[n]:=Search(convert(a[n-1], string), G)-1:printf("%d, ", a[n-1]):od: # Nathaniel Johnston, Apr 30 2011

Formula

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

A098327 Recurrence sequence derived from the decimal places of sqrt(e).

Original entry on oeis.org

0, 9, 60, 79, 59, 137, 479, 2897, 1397, 24474, 63515, 71287, 191542, 1432289, 1766633, 1380465, 2894629, 1464385, 10676561
Offset: 1

Views

Author

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

Keywords

Comments

a(20) > 5*10^7.

Examples

			sqrt(e)=1.6487212707001281468...
So for example, with a(1)=0, a(2)=9 because 9th decimal place is 0; a(3)=60 because 9 appears at decimal place number 60 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), A098326 for sqrt(2).

Formula

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

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

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

			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.

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).

Programs

  • 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

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).

Extensions

More terms from Ryan Propper, Jul 21 2006

A120482 Recurrence sequence derived from the digits of the square root of 3 after its decimal point.

Original entry on oeis.org

0, 4, 22, 215, 2737, 8636, 20805, 38867, 1868, 6505, 5767, 1004, 1216, 11702, 55995, 43202, 314308, 2100749, 2420235, 7750204, 5141127, 2950527, 3113789, 42198, 119161, 96031, 77643, 10695, 105061, 37099, 176209, 3390478, 4549989, 9038843
Offset: 0

Views

Author

Ryan Propper, Jul 21 2006

Keywords

Examples

			sqrt(3) = 1.73205080756887729352744634151...
So for example, with a(0) = 0, a(1) = 4 because the 4th digit after the decimal point is 0; a(2) = 22 because the 22nd digit after the decimal point is 4 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), A098326 for sqrt(2), A189893 for sqrt(5), A098327 for sqrt(e), A098328 for 2^(1/3).

Programs

  • Maple
    with(StringTools): Digits:=10000: G:=convert(evalf(sqrt(3)),string): a[0]:=0: for n from 1 to 6 do a[n]:=Search(convert(a[n-1],string), G)-2:printf("%d, ",a[n-1]):od: # Nathaniel Johnston, Apr 30 2011

Formula

a(0) = 0; for i >= 0, a(i+1) = position of first occurrence of a(i) in decimal places of sqrt(3).

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

Original entry on oeis.org

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

Views

Author

Nathaniel Johnston, Apr 30 2011

Keywords

Examples

			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.

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).

Programs

  • 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:

Formula

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

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