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 14 results. Next

A091658 When A032523 is a maximum; or, A091657 less duplicates.

Original entry on oeis.org

4, 9, 30, 40, 44, 130, 276, 647, 791, 878, 1008, 3041, 3200, 3384, 5606, 9721, 17899, 22640, 34070, 34152, 37648, 91193, 134943, 152617, 158172, 190950, 258992, 315679, 525765, 558041, 734305, 1500708, 1669873, 1873804, 1936902, 4278672, 5227319, 7385934, 7876549, 10765774, 11396841, 11466234, 12994613, 19147251, 31403937, 43166470
Offset: 1

Views

Author

Robert G. Wilson v, Jan 26 2004

Keywords

Comments

Each entry is enumerated: 1,2,1,2,1,1,2,6,8,4,1,1,1,1,1,1,1,1,1,8,6,... in A091657.
The 4278672nd term of the continued fraction expansion of Pi is 837.

Examples

			One has to go to the 30th term of the continued fraction of Pi (4) to have seen the integers 1, 2, 3 & 4.

Links

Crossrefs

Cf. A001203, A032523, A091657.

Programs

  • Mathematica
    cfpi = ContinuedFraction[Pi, 10000000]; a = Table[0, {1562}]; Do[b = cfpi[[n]]; If[b < 1563 && a[[b]] == 0, a[[b]] = n], {n, 1, 10000000}]; c

A033165 First occurrence of n as a term in the continued fraction for zeta(3).

Original entry on oeis.org

1, 12, 25, 2, 64, 27, 17, 140, 10, 119, 21, 239, 175, 78, 181, 46, 200, 4, 83, 619, 753, 412, 177, 197, 414, 138, 146, 561, 233, 29, 2276, 1549, 660, 889, 298, 1040, 2279, 322, 1274, 1882, 345, 2926, 673, 254, 1961, 1542, 1681, 296, 5423, 2423, 2557, 228
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Incorrectly indexed version of A229057.

Links

Crossrefs

Cf. A013631, A032523, A229057.

Programs

  • Mathematica
    With[{cfz3 = ContinuedFraction[Zeta[3], 6000]}, Flatten[Table[Position[cfz3, n, 1, 1], {n, 60}]]] (* Harvey P. Dale, Nov 11 2012 *)
  • PARI
    /* 1500 precision digits */ v=contfrac(zeta(3)); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

Formula

a(n) = 1 + A229057(n).

Extensions

More terms from Randall L Rathbun, Feb 03 2002

A107892 Index of first occurrence of n-th prime in A001203, the continued fraction for Pi.

Original entry on oeis.org

9, 1, 40, 2, 276, 28, 647, 140, 203, 243, 878, 784, 754, 492, 825, 1547, 907, 868, 1789, 9215, 898, 6222, 9131, 4829, 1516, 6700, 22640, 872, 11170, 3204, 223, 10387, 8299, 30086, 31079, 12637, 8486, 20644, 8451, 53069, 32093, 16297, 20276, 1002, 21264
Offset: 1

Views

Author

Zak Seidov, May 25 2005

Keywords

Comments

Until it is proved that every prime does indeed occur in A001203, we should tacitly understand a convention like "A107892(n) = 0 if A000040(n) does not occur in A001203". - M. F. Hasler, Mar 31 2008
Among first 1000000 terms of the continued fraction for Pi, the first absent primes have indices 129, 132, 137, 146, 147, 158, 160, 165, 170, 172, 175, 180, 182, 184, 189, 193, 197, 198, 199. The 200th prime is in the 947040th place, thus A107892(200)=947040.

Links

Crossrefs

Cf. A032523: first occurrence of n in A001203.
Cf. A138758, A138759.

Formula

A107892(n) = A032523(A000040(n)) = min { k | A001203(k)=A000040(n) }. - M. F. Hasler, Mar 31 2008

Extensions

Edited by M. F. Hasler, Mar 31 2008

A033149 Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).

Original entry on oeis.org

2, 4, 9, 8, 11, 69, 24, 14, 139, 52, 22, 161, 10, 199, 337, 79, 163, 176, 384, 614, 183, 651, 137, 480, 250, 862, 554, 618, 287, 300, 1952, 166, 150, 2038, 560, 483, 1284, 681, 306, 20, 349, 1130, 2280, 1884, 1903, 2564, 4753, 717, 31, 2610, 568, 248, 2171
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

The smallest positive integers not appearing in the first 970,258,158 terms of the c.f. are 13161, 13295, 14734, 14970, 14971, 15795, 15985, 16011, 16110, ... - Eric W. Weisstein, Sep 21 2011

Links

Crossrefs

Cf. A001620, A002852, A032523.
Cf. A224847 (= a(n) -1).

Programs

  • Mathematica
    With[{cf=ContinuedFraction[EulerGamma,5000]},Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Aug 06 2025 *)
  • PARI
    /* 15000 precision digits */ v=contfrac(Euler); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

Formula

a(n) = A224847(n) + 1.

Extensions

More terms from Benoit Cloitre, Oct 20 2002

A225802 Position of first occurrence of n in continued fraction for Pi, or -1 if n never occurs.

Original entry on oeis.org

3, 8, 0, 29, 39, 31, 1, 43, 129, 99, 275, 54, 27, 12, 2, 77, 646, 136, 139, 179, 213, 82, 202, 90, 790, 111, 573, 174, 242, 146, 877, 454, 530, 420, 1007, 593, 783, 3040, 720, 1871, 753, 118, 491, 428, 80, 3199, 824, 282, 3026, 464, 1436, 3383, 1546, 1863, 445, 1017
Offset: 1

Views

Author

Eric W. Weisstein, Jul 27 2013

Keywords

Comments

Correctly indexed version of A032523.
All positive integers <= 49003 occur in the first 15000000000 terms of the c.f. (the first that do not are 49004, 50471, 53486, 56315, 58255, ...) - Eric W. Weisstein, Jul 27 2013

Examples

			The continued fraction of Pi is [a_0; a_1, a_2, ...] = [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, ...], so
a(1) = 3 (1 first occurs at term a_3);
a(2) = 8 (2 first occurs at term a_8);
a(3) = 0 (3 first occurs at term a_0).

Links

Crossrefs

Cf. A032523 (= a(n) + 1).
Cf. A001203 (continued fraction of Pi).

Formula

a(n) = A032523(n) - 1.

Extensions

"Escape clause" added to definition by Jianing Song, Apr 06 2019

A091657 Length of the smallest prefix of the continued fraction expansion for Pi that includes each of 1..n.

Original entry on oeis.org

4, 9, 9, 30, 40, 40, 40, 44, 130, 130, 276, 276, 276, 276, 276, 276, 647, 647, 647, 647, 647, 647, 647, 647, 791, 791, 791, 791, 791, 791, 878, 878, 878, 878, 1008, 1008, 1008, 3041, 3041, 3041, 3041, 3041, 3041, 3041, 3041, 3200, 3200, 3200, 3200, 3200, 3200
Offset: 1

Views

Author

Robert G. Wilson v, Jan 26 2004

Keywords

Crossrefs

Cf. A001203, A032523.

Programs

  • Mathematica
    f[n_] := Block[{k = 1}, While[ StringPosition[ ToString[ Union[ ContinuedFraction[Pi, k]]], StringDrop[ ToString[ Table[i, {i, n}]], -1]] == {}, k++ ]; k]; Table[ f[n], {n, 1, 51}]

Formula

a(n) = max(A032523(n), a(n-1)) for n > 1. - Andrew Howroyd, Aug 05 2024

Extensions

Name clarified by Andrew Howroyd, Aug 05 2024

A076587 First occurrence of n as a term in the continued fraction for Pi/2.

Original entry on oeis.org

1, 10, 4, 9, 20, 13, 26, 11, 142, 102, 70, 93, 179, 69, 127, 283, 52, 1166, 141, 605, 100, 83, 280, 414, 451, 61, 30, 234, 848, 448, 5, 372, 1389, 2445, 2082, 498, 603, 2565, 517, 3715, 22, 1155, 419, 856, 4125, 1573, 441, 207, 42, 1536, 5359, 576, 6654, 1002
Offset: 1

Views

Author

Benoit Cloitre, Oct 20 2002

Keywords

Crossrefs

Cf. A032523, A053300.

Programs

  • Mathematica
    Module[{nn=6700,p2},p2=ContinuedFraction[Pi/2,nn];Table[Position[p2,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Jul 14 2023 *)
  • PARI
    default(realprecision, 1500); v=contfrac(Pi/2); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

A076588 First occurrence of n as a term in the continued fraction for Pi/4.

Original entry on oeis.org

2, 8, 3, 76, 17, 67, 50, 54, 11, 20, 73, 413, 59, 162, 7, 75, 13, 587, 393, 24, 112, 228, 403, 40, 843, 560, 590, 69, 187, 617, 215, 400, 1182, 259, 1680, 548, 758, 226, 133, 78, 1265, 589, 96, 169, 3108, 5892, 258, 261, 4608, 3810, 2386, 1251, 2698, 2374
Offset: 1

Views

Author

Benoit Cloitre, Oct 20 2002

Keywords

Crossrefs

Cf. A032523, A070989.

Programs

  • Mathematica
    With[{cf=ContinuedFraction[Pi/4,6000]},Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Aug 25 2025 *)
  • PARI
    \\ 15000 precision digits
v=contfrac(Pi/4); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

A076589 First occurrence of n as a term in the continued fraction for sqrt(Pi).

Original entry on oeis.org

1, 4, 3, 20, 43, 7, 32, 54, 40, 86, 91, 29, 10, 363, 705, 169, 341, 14, 181, 81, 307, 574, 153, 234, 175, 477, 552, 9, 2550, 743, 801, 2245, 239, 360, 402, 44, 1985, 1682, 395, 1074, 331, 285, 1278, 2097, 384, 3972, 857, 2240, 146, 9736, 924, 1690, 350, 1445
Offset: 1

Views

Author

Benoit Cloitre, Oct 20 2002

Keywords

Crossrefs

Cf. A032523, A058280.

Programs

  • PARI
    default(realprecision, 1500); v=contfrac(sqrt(Pi)); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

A076590 First occurrence of n as a term in the continued fraction for zeta(2)=Pi^2/6.

Original entry on oeis.org

1, 6, 12, 5, 37, 23, 8, 56, 83, 14, 107, 128, 111, 121, 20, 171, 346, 172, 57, 45, 607, 641, 968, 925, 239, 291, 44, 659, 396, 233, 186, 1353, 509, 739, 843, 681, 1020, 213, 577, 345, 670, 196, 287, 91, 54, 3510, 910, 800, 3462, 803, 503, 355, 3428, 1157, 247
Offset: 1

Views

Author

Benoit Cloitre, Oct 20 2002

Keywords

Crossrefs

Cf. A013679, A032523.

Programs

  • Mathematica
    Module[{nn=4000,cf},cf=ContinuedFraction[Pi^2/6,nn];Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Dec 29 2024 *)
  • PARI
    /* 15000 precision digits */ v=contfrac(zeta(2)); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)
Showing 1-10 of 14 results. Next

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

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