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 1-9 of 9 results.

A090897 Next n digits of Pi.

Original entry on oeis.org

3, 14, 159, 2653, 58979, 323846, 2643383, 27950288, 419716939, 9375105820, 97494459230, 781640628620, 8998628034825, 34211706798214, 808651328230664, 7093844609550582, 23172535940812848, 111745028410270193, 8521105559644622948, 95493038196442881097
Offset: 1

Views

Author

Michael Joseph Halm, Feb 26 2004

Keywords

Comments

More precisely: the integer resulting from reading the "next n digits of Pi" in base 10, so leading zeros cannot be directly seen, but easily be "reconstructed" from the fact that the term will have less than n digits although it is made from n digits of Pi. - M. F. Hasler, Jan 06 2023
It seems that all terms have at least one prime factor that does not appear in the combined list of prime factors of the preceding terms of the sequence. - Mario Cortés, Aug 20 2020 [Checked up to n=65. - Michel Marcus, Aug 21 2020]

Examples

			a(3) = 159 because after the first (a(1) = 3) and the next two digits of Pi (a(2) = 14) the next three are 159.
From _Aaron T Cowan_, Jan 03 2023: (Start)
Other examples are as follows and fall into a triangular digit pattern, though there is no guarantee that they will remain triangular in all cases
  a(1) = 3;
  a(2) = 14;
  a(3) = 159;
  a(4) = 2653;
  a(5) = 58979;
   (End)
Indeed, precisely whenever A086639(n) = 0, then the corresponding term of this sequence will lack one or more leading zeros and therefore the above list will deviate from the triangular shape. - _M. F. Hasler_, Jan 06 2023

Links

Crossrefs

Cf. A000796 (Pi), A016062, A081368, A086639.

Programs

  • Maple
    Partitioner := proc(cons, len) local i, R, spl; R := []; i:=0;
spl := L -> [seq([seq(L[i], i=1 + n*(n+1)/2..(n+1)*(n+2)/2)], n=0..len)]:
ListTools:-Reverse(convert(floor(cons*10^((len+1)*(len+2)/2)), base, 10)):
map(`@`(parse, cat, op), spl(%)) end:
aList := -> Partitioner(Pi, 20); aList(20); # Peter Luschny, Aug 22 2020
  • Mathematica
    With[{pi=RealDigits[Pi,10,500][[1]]},FromDigits/@Table[Take[pi,{n (n-1)/2+1, (n(n+1))/2}],{n,25}]] (* Harvey P. Dale, Dec 24 2011 *)
  • PARI
    lista(nn) = {my(nd = 5+nn*(nn+1)/2); default(realprecision, nd); my(vd = digits(floor(Pi*10^nd))); my(pos = 1); my(vr = vector(nn)); for (n=1, nn, vr[n] = fromdigits(vector(n, k, vd[k+ pos-1])); pos += n;); vr;} \\ Michel Marcus, Aug 21 2020

Formula

a(n) = floor( Pi * 10^(n*(n+1)/2-1) ) mod (10^n). - Carl R. White, Aug 13 2010

A037244 Base 100 expansion of Pi.

Original entry on oeis.org

3, 14, 15, 92, 65, 35, 89, 79, 32, 38, 46, 26, 43, 38, 32, 79, 50, 28, 84, 19, 71, 69, 39, 93, 75, 10, 58, 20, 97, 49, 44, 59, 23, 7, 81, 64, 6, 28, 62, 8, 99, 86, 28, 3, 48, 25, 34, 21, 17, 6, 79, 82, 14, 80, 86, 51, 32, 82, 30, 66, 47, 9, 38, 44, 60, 95, 50, 58, 22, 31
Offset: 0

Views

Author

Chung Wa, Ho (chungwa(AT)netvigator.com)

Keywords

Comments

Start with 3; other terms are formed from pairs of successive digits in decimal expansion of Pi.

Examples

			Pi = 3.14159265358979323846264338327950288419716939937510582...

Links

Crossrefs

Cf. A000796, A016062, A035331.

Programs

  • Mathematica
    Module[{A037244 = {}, p = N[Pi, 139]},
 Do[Module[{temp = IntegerPart[p]}, AppendTo[A037244, temp];
   p = 100 (p - temp);], {70}]; A037244]

Extensions

Better definition from Franklin T. Adams-Watters, Apr 10 2006

A050819 Increasing odd numbers seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct.

Original entry on oeis.org

3, 141, 59265, 358979, 3238462643, 3832795028841, 97169399375105, 820974944592307, 81640628620899862803, 48253421170679821480865, 132823066470938446095505, 82231725359408128481117450284102701, 9385211055596446229489549303819644288109
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Comments

Leading zero not allowed thus forcing continuation of previous term.

Links

Crossrefs

Cf. A000796, A016062, A037244, A047777, A050817, A016062, A050818, A050807.

Extensions

a(12) corrected and a(13) from Sean A. Irvine, Aug 19 2021

A008829 Smallest number a(n) formed from consecutive sequences of digits of Pi and satisfying a(n) > a(n-1); first 3 is omitted.

Original entry on oeis.org

1, 4, 15, 92, 653, 5897, 9323, 84626, 433832, 795028, 841971, 6939937, 51058209, 74944592, 307816406, 2862089986, 28034825342, 1170679821480, 8651328230664, 70938446095505, 82231725359408, 128481117450284, 1027019385211055
Offset: 1

Views

Author

N. J. A. Sloane. This sequence appeared in the 1973 "Handbook", but was then dropped from the database. Resubmitted by Victor H. Auerbach (vhambler(AT)voicenet.com). Entry revised by N. J. A. Sloane, Jun 11 2012

Keywords

Comments

Terms are not permitted to start with a 0, so when this would otherwise occur the 0 must be included in the previous term, for example, a(18). - Sean A. Irvine, Apr 07 2018

References

  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

Crossrefs

Cf. A000796. Apart from the two initial terms equals A016062.

Programs

  • Mathematica
    pi = Rest@ RealDigits[Pi, 10, 2500][[1]]; a[0] = 0; a[n_] := a[n] = Block[{k = 1}, While[ FromDigits[ Take[pi, {1, k}]] < a[n - 1], k++]; While[ pi[[k + 1]] == 0, k++]; b = FromDigits[Take[pi, {1, k}]]; pi = Drop[pi, k]; b]; Array[a, 50] (* Robert G. Wilson v, Apr 08 2018 *)

Extensions

a(19)-a(20) corrected and more terms from Sean A. Irvine, Apr 07 2018

A035331 Base-1000 expansion of Pi.

Original entry on oeis.org

3, 141, 592, 653, 589, 793, 238, 462, 643, 383, 279, 502, 884, 197, 169, 399, 375, 105, 820, 974, 944, 592, 307, 816, 406, 286, 208, 998, 628, 34, 825, 342, 117, 67, 982, 148, 86, 513, 282, 306, 647, 93, 844, 609, 550, 582, 231, 725, 359, 408, 128, 481, 117, 450
Offset: 0

Views

Author

Jörg Zurkirchen

Keywords

Comments

Start with a(0)=3; other terms are formed from triples of successive digits in the decimal expansion of Pi.
This sequence can be considered as a (pseudo)random generator with range 0..999. Its scatterplot graph is very similar to that of other random generators, e.g., A096558. - M. F. Hasler, May 14 2015

Examples

			Pi = 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 ...

Links

Crossrefs

Cf. A000796, A016062, A037244, A050819, A032445, A064467.

Programs

  • Mathematica
    RealDigits[Pi,1000,60][[1]] (* Harvey P. Dale, Nov 22 2015 *)
  • PARI
    default(realprecision,3*N=100);vector(N,i,Pi\1000^(1-i)%1000) \\ or: {P=Pi;vector(N,i,P\1+0*P=frac(P)*1000)} or {P=Pi/1000;vector(N,i,floor(P=frac(P)*1000))}. \\ M. F. Hasler, May 11 2015

Formula

a(n) = floor(Pi*10^(3n)) mod 1000. - M. F. Hasler, May 14 2015

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 04 2001
Better definition from Franklin T. Adams-Watters, Apr 10 2006

A050807 Increasing even numbers seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct.

Original entry on oeis.org

314, 1592, 65358, 97932, 384626, 433832, 795028, 8419716, 939937510, 5820974944, 59230781640, 62862089986, 280348253421170, 679821480865132, 8230664709384460, 955058223172535940, 8128481117450284102, 70193852110555964462, 2948954930381964428810
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Comments

Leading zero not allowed thus forcing continuation of previous term.

Links

Crossrefs

Cf. A000796, A047777, A050817, A016062, A050818, A050819.

Extensions

More terms from Sean A. Irvine, Aug 19 2021

A050818 Even numbers seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct.

Original entry on oeis.org

314, 1592, 6, 5358, 97932, 38, 4, 62, 64, 338, 32, 7950, 2, 8, 84, 19716, 939937510, 58, 20, 974, 94, 4592, 30, 78, 16, 40, 628, 620, 8998, 6280, 34, 82, 534, 21170, 6798, 214, 80, 86, 5132, 8230, 66, 470, 938, 44, 60, 9550, 582, 23172, 53594, 0, 812, 848
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Comments

Leading zero not allowed thus forcing continuation of previous term.

Links

  • C. Rivera, Problem 18, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A047777, A050817, A016062, A050819, A050807.

A050817 Odd numbers seen in decimal expansion of Pi (disregarding the decimal period) contiguous, smallest and distinct.

Original entry on oeis.org

3, 1, 41, 5, 9, 265, 35, 89, 7, 93, 23, 8462643, 383, 27, 95028841, 97, 169, 39, 937, 5105, 8209, 749, 445, 92307, 81, 64062862089, 9862803, 4825, 3421, 17067, 9821, 480865, 13, 28230664709, 3844609, 5505, 8223, 17, 25, 359, 4081, 28481, 11
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1999

Keywords

Comments

Leading zero not allowed thus forcing continuation of previous term.

Links

  • C. Rivera, Problem 18, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A047777, A050818, A016062, A050819, A050807.

A098711 Write down decimal expansion of Pi; starting with 31, divide up into chunks of minimal length so that chunks are increasing numbers and do not begin with 0.

Original entry on oeis.org

31, 41, 59, 265, 358, 979, 3238, 4626, 43383, 279502, 884197, 1693993, 75105820, 97494459, 230781640, 628620899, 862803482, 5342117067, 9821480865, 132823066470, 938446095505, 8223172535940, 81284811174502, 84102701938521
Offset: 1

Views

Author

Alexandre Wajnberg, Sep 28 2004

Keywords

Comments

Seems to grow slower than A016062 (another sequence built on the same principle, which begins with 3, 14, 15, 92, 653...).

Examples

			a(4) = 265, the three digits of Pi following a(3) = 59, because neither 2 nor 26 is > 59. a(13) = 75105820 even though 7510582 > a(12), because a(14) may not begin with a 0.

Crossrefs

Cf. A000796, A037244, A035331.

Extensions

Edited and extended by David Wasserman, Feb 26 2008
Showing 1-9 of 9 results.

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

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