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 1-10 of 20 results. Next

A098289 Let a(1)=0. Then a(i+1)=position of first occurrence of a(i) in decimal expansion of log 2.

Original entry on oeis.org

0, 9, 2, 22, 419, 591, 898, 915, 285, 3618, 10367, 5396, 1192, 8251, 13198, 16050, 47987, 146191, 2518028, 7744270, 16819386
Offset: 1

Views

Author

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

Keywords

Examples

			log 2 = 0.693147180559945309417232121458...
For example, a(2)=9 because the 9th digit of log 2 after decimal point is 0 and this is the first occurrence of 0.
a(3)=2 because 2nd decimal digit of log 2 is 9, a(4)=22 because 22nd decimal digit of log 2 is 2 and so on.

Crossrefs

Cf. A098266 (for e recurrence), A097614 (for Pi recurrence).

Extensions

Edited by N. J. A. Sloane, Oct 15 2006
More terms from Charles R Greathouse IV, Oct 09 2006

A098266 a(1)=0; for i>=1, a(i+1)=position of first occurrence of a(i) in decimal expansion of e.

Original entry on oeis.org

0, 13, 27, 62, 32, 110, 3188, 12078, 141356, 2085932, 3497082, 4910326, 929922, 1189814, 4196683, 1301478, 19560712, 6894489, 41960008
Offset: 0

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 01 2004

Keywords

Comments

Recurrence sequence based on positions of digits in decimal places of e.

Examples

			So for example, a(2)=13 because 13th digit of e after decimal point is 0.
a(3)=27 because 27th decimal digit of e is 13, a(4)=62 because 62nd to 63rd decimal digits of e form "13" and so on.

Crossrefs

Cf. A078197 for the first occurrence of integers in decimal digits of e; A097614 for the analogous recurrence sequence for Pi, also A014777 for positions of integers in decimal digits of Pi.

Extensions

More terms from Ben Ross (bmr180(AT)psu.edu), Feb 01 2006

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).

A098319 a(1)=0, and a(n+1) is the position of first occurrence of a(n) in the decimal expansion of 1/Pi.

Original entry on oeis.org

0, 5, 19, 41, 717, 925, 358, 1004, 5044, 6981, 2520, 7559, 139, 694, 919, 40, 36, 126, 663, 1745, 3950, 12447, 18530, 22257, 82998, 27887, 5940, 1387, 3601, 2344, 2795, 2422, 49157, 6577, 5816, 10987, 36519, 334412, 153716, 1055197, 11437580
Offset: 1

Views

Author

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

Keywords

Comments

The equivalent sequence for Zeta(3) repeated after very few terms. When, if ever, does this sequence start to repeat?

Examples

			1/Pi = 0.31830988618379067153...
a(1)=0; a(2)=5 because the 5th decimal digit after the "0." is 0; a(3)=19 because the 19th digit is 5, etc.

Crossrefs

Cf. A098266 (for e version), A097614 (for Pi version), A098289 (for log(2) version), A098290 (for Zeta(3) version), A049541 for digits of 1/Pi.

Extensions

a(38)-a(39) from Nathaniel Johnston, Apr 30 2011
a(40) and a(41) from D. S. McNeil, Aug 27 2011

A098320 a(1)=0; for i>=1, a(i+1)=position of first occurrence of a(i) in decimal expansion of 1/e.

Original entry on oeis.org

0, 27, 88, 308, 267, 922, 811, 40, 150, 173, 555, 1751, 3389, 5859, 10579, 227865, 560966, 1382684, 12331649, 118447869
Offset: 0

Views

Author

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

Keywords

Comments

Recurrence sequence based on positions of digits in decimal places of 1/e.

Examples

			So for example, a(2)=27 because 27th digit of 1/e after decimal point is 0.
a(3)=88 because 88th decimal digit of 1/e is where 27 appears,
a(4)=308 because 308th to 309th decimal digits of 1/e form "88" and so on.

Crossrefs

Cf. A097614 for the analogous recurrence sequence for Pi, A098266 for e recurrence, A098289 for log(2) recurrence, A098290 for Zeta(3) recurrence, A098319 for 1/Pi recurrence. See A068985 for digits of 1/e.

Extensions

More terms from Ben Ross (bmr180(AT)psu.edu), Feb 01 2006

A098321 Recurrence sequence based on positions of digits in decimal places of gamma, the Euler-Mascheroni constant.

Original entry on oeis.org

0, 11, 233, 223, 1080, 2631, 19161, 318674, 269389, 609124, 97349, 125496, 2611514, 6766458, 2093818, 4312197, 4284994, 7170002, 567295, 234495, 1574091, 1722475, 6848664, 777039, 637036, 1367169, 8195403, 3747746, 21147798, 2053675, 6009248, 12095, 312755, 1205372, 15773902, 139394774, 169096914
Offset: 0

Views

Author

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

Keywords

Examples

			So for example, a(2)=11 because 11th digit of gamma after decimal point is 0.
a(3)=233 because 233rd decimal digit of gamma is where 11 appears, a(4)=223 because 223rd to 225th digits of gamma form "233" 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. See A001620 for gamma digits.

Formula

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

Extensions

More terms from Charles R Greathouse IV, Sep 25 2008

A098322 Recurrence sequence based on positions of digits in decimal places of Catalan's constant, G (often also called K).

Original entry on oeis.org

0, 16, 48, 101, 421, 2374, 7728, 9449, 17685, 83666, 71168, 128130, 555251, 412816, 271385, 1111695, 1910101, 11633401, 14851698, 9668058, 43227391, 159078942
Offset: 0

Views

Author

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

Keywords

Examples

			So for example, a(2)=16 because 16th digit of G is 0.
a(3)=48 because 16 appears at the 48th-49th digits of G, a(4)=101 because the 101st to 102nd digits of G form "48" 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. A006752 for digits of Catalan's constant.

Formula

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

Extensions

14 more terms. 159078942 does not occur within first 2 billion digits of Catalan's constant. Sean A. Irvine, Sep 02 2009

A098323 Recurrence sequence based on positions of digits in decimal places of 1/G, where G is Catalan's constant (also often called K).

Original entry on oeis.org

0, 1, 3, 9, 2, 33, 27, 82, 48, 162, 279, 1140, 5727, 20729, 717726, 430977, 1112328
Offset: 0

Views

Author

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

Keywords

Examples

			1/G=1.091744063703906101454159473...
So for example, a(2)=1 because first decimal place of 1/G is 0.
a(3)=3 because 3rd decimal place of 1/G is 1, a(4)=9 because the 9th decimal place of 1/G is 3 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.

Formula

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

Extensions

a(13) from Nathaniel Johnston, Apr 30 2011
a(14)-a(16) from D. S. McNeil, Oct 01 2011

A098324 Recurrence sequence based on positions of digits in decimal places of phi, the Golden Ratio = (1+sqrt(5))/2.

Original entry on oeis.org

0, 4, 11, 34, 26, 67, 150, 1485, 2497, 8001, 2773, 16668, 39567, 80705, 15643, 19267, 29310, 223602, 2318795, 9376463, 7972671, 2412975, 3754694, 9560425, 1910435
Offset: 0

Views

Author

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

Keywords

Examples

			phi=1.61803398874989484820...
So for example, a(2)=4 because 4th decimal place of phi is 0.
a(3)=11 because 11th decimal place of phi is 4, a(4)=34 because 11 appears at the 34th to 35th decimal places 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.

Programs

  • Maple
    with(StringTools): Digits:=100000: G:=convert(evalf((1+sqrt(5))/2),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: # Nathaniel Johnston, Apr 30 2011

Formula

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

Extensions

a(17)-a(24) from Nathaniel Johnston, Apr 30 2011

A098325 Recurrence sequence based on positions of digits in decimal places of sqrt(Pi).

Original entry on oeis.org

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

Views

Author

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

Keywords

Examples

			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.

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).

Programs

  • 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

Formula

a(1)=0, p(i)=position of first occurrence of a(i) in decimal places of sqrt(Pi), a(i+1)=p(i).
Showing 1-10 of 20 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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