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 1-8 of 8 results.

A096567 First digit to appear n times in the base-10 expansion of Pi.

Original entry on oeis.org

3, 1, 5, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 8, 2, 2, 8, 2, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Matthew Vandermast, Jun 26 2004

Keywords

Comments

The number 7 finally appears as a(32344). - T. D. Noe, Sep 13 2012
The number 6 appears for the first time as a(99032274). - Kester Habermann, Feb 01 2021

Examples

			a(3) = 5 because 5 is the first digit to appear 3 times in the decimal expansion of Pi = 3.141(5)926(5)3(5)... - _Bobby Jacobs_, Aug 30 2017

Links

Crossrefs

Cf. A000796, A014976, A053745-A053753, A096566.
Cf. A195138, A195139, A195141, A280811.
Cf. A276686, A276992, A276993, A277171, A291599, A291600.

Programs

  • Mathematica
    nn = 1000; t = {}; d = RealDigits[Pi, 10, nn][[1]]; dCnt = Table[0, {10}]; cnt = 1; Do[b = ++dCnt[[1 + d[[n]]]]; If[b == cnt, AppendTo[t, d[[n]]]; cnt++], {n, nn}]; t (* T. D. Noe, Sep 13 2012 *)

Extensions

More terms from David Wasserman, Nov 16 2007

A276993 First 3-digit number to appear n times in the decimal expansion of Pi.

Original entry on oeis.org

314, 592, 446, 117, 105, 19, 381, 279, 609, 609, 848, 848, 654, 654, 654, 654, 19, 19, 965, 965, 965, 965, 19, 19, 19, 494, 564, 390, 390, 390, 390, 390, 682, 682, 390, 346, 390, 390, 390, 390, 390, 390, 346, 346, 346, 99, 201, 201, 201, 201, 201, 201, 201
Offset: 1

Views

Author

Bobby Jacobs, Sep 24 2016

Keywords

Comments

a(6) is the 3-digit number 019.
By the pigeonhole principle, it suffices to examine 1000n - 997 digits of Pi to find the n-th term; on average 1000n - O(sqrt n) will suffice. Do each of 0..999 appear in this sequence? Which appears last? - Charles R Greathouse IV, Sep 26 2016

Examples

			a(2) = 592 because 592 is the first 3-digit number to appear 2 times in the decimal expansion of Pi = 3.141(592)653589793238462643383279502884197169399375105820974944(592)...

Links

Crossrefs

Cf. A000796, A096567, A276686, A276992, A277171, A290643, A291599, A291600.

Extensions

More terms from Alois P. Heinz, Oct 02 2016

A276686 First 4-digit number to appear n times in the decimal expansion of Pi.

Original entry on oeis.org

3141, 582, 9999, 2796, 6549, 2019, 2916, 8352, 5485, 5485, 5485, 5485, 5485, 5485, 5485, 1177, 1177, 5485, 1177, 3718, 5485, 5485, 1766, 1766, 5485, 4608, 4608, 4608, 4608, 4608, 5485, 5485, 504, 504, 504, 504, 504, 504, 504, 2103, 504, 504, 9479, 504, 504
Offset: 1

Views

Author

Bobby Jacobs, Sep 25 2016

Keywords

Comments

Note that the sequence contains elements whose number of digits is less than 4. See example.
The first 3 appearances of a(3) = 9999 overlap in 999999.

Examples

			a(2) = 582 because "0582" is the first 4-digit number to appear 2 times in the decimal expansion of Pi = 3.1415926535897932384626433832795028841971693993751(0582)097494459230781\ 640628620899862803482534211706798214808651328230664709384460955(0582)...

Crossrefs

Cf. A000796, A096567, A276992, A276993, A277171, A290644, A291599, A291600.

Extensions

More terms from Alois P. Heinz, Oct 02 2016

A277171 First 5-digit number to appear n times in the decimal expansion of Pi.

Original entry on oeis.org

31415, 60943, 48940, 36041, 86538, 85990, 40230, 91465, 26063, 87258, 87258, 87258, 56517, 15157, 47392, 15157, 87258, 87258, 15157, 15157, 46083, 46083, 46083, 46083, 15931, 15931, 10767, 10767, 10767, 18804, 18804, 83903, 83903, 83903, 18271, 83903, 83903
Offset: 1

Views

Author

Bobby Jacobs, Oct 02 2016

Keywords

Examples

			a(2) = 60943 because 60943 is the first 5-digit number to appear 2 times in the decimal expansion of Pi.

Crossrefs

Cf. A000796, A096567, A276686, A276992, A276993, A291599, A291600.

Extensions

More terms from Alois P. Heinz, Oct 02 2016

A291599 First 6-digit number to appear n times in the decimal expansion of Pi.

Original entry on oeis.org

314159, 949129, 266830, 178653, 872117, 872117, 872117, 919441, 919441, 735287, 820737, 420516, 802307, 556505, 267638, 107072
Offset: 1

Views

Author

Bobby Jacobs, Aug 27 2017

Keywords

Comments

The first 2 appearances of a(2) = 949129 both end at the beginning of a block of 100 digits of Pi after the decimal point. The 5th block of 100 digits of Pi after the decimal point ends with 94912, and the 6th block of 100 digits starts with 9. The 13th block of 100 digits of Pi after the decimal point ends with 94912, and the 14th block of 100 digits starts with 9.

Examples

			a(2) = 949129 because 949129 is the first 6-digit number to appear 2 times in the decimal expansion of Pi.

Crossrefs

Cf. A000796, A096567, A276686, A276992, A276993, A277171, A291600.

Extensions

a(11)-a(16) added by Alois P. Heinz, Aug 28 2017

A291600 First 10-digit number to appear n times in the decimal expansion of Pi.

Original entry on oeis.org

3141592653, 4392366484, 9526413073, 7454969632, 1459184231, 3955267283
Offset: 1

Views

Author

Bobby Jacobs, Aug 27 2017

Keywords

Comments

This sequence was mentioned in a forum post called "Ten repeating numbers in Pi". It was about finding a 10-digit number that repeated in Pi. The answer was a(2) = A197123(10) = 4392366484.

Examples

			a(2) = 4392366484 because 4392366484 is the first 10-digit number to appear 2 times in the decimal expansion of Pi.

Links

Crossrefs

Cf. A000796, A096567, A197123, A276686, A276992, A276993, A277171, A291599.

Extensions

a(5)-a(6) from Michael S. Branicky, Sep 04 2024

A277270 First 2-digit number to appear n times in the decimal expansion of e.

Original entry on oeis.org

27, 18, 28, 35, 66, 66, 66, 74, 7, 74, 74, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 93, 25, 25, 25, 25, 44, 25, 44, 44, 44, 44, 96, 96, 63, 63, 25, 96, 25, 96, 63, 63, 63, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36
Offset: 1

Views

Author

Bobby Jacobs, Nov 05 2016

Keywords

Comments

a(9) is the 2-digit number 07.

Examples

			a(2) = 18 because 18 is the first 2-digit number to appear 2 times in the decimal expansion of e = 2.7(18)28(18)...

Links

Crossrefs

Cf. A001113, A195138, A276992, A290643, A290644.

A361131 Let d = A096567(n) be the first digit to appear n times in the decimal expansion of Pi; if d is the m-th digit of Pi, a(n) = m.

Original entry on oeis.org

1, 4, 11, 18, 25, 26, 28, 44, 47, 59, 63, 80, 81, 101, 108, 114, 125, 135, 148, 151, 153, 162, 172, 187, 198, 205, 206, 223, 229, 234, 237, 256, 268, 274, 279, 294, 297, 304, 322, 335, 338, 355, 374, 381, 387, 393, 401, 433, 438, 439, 443, 446, 447, 472, 484, 491, 495
Offset: 1

Views

Author

N. J. A. Sloane, Mar 11 2023

Keywords

Examples

			Pi = 3.14159265358979323...
The first digit to appear 4 times in Pi is 3, at the 18th digit, so a(4) = 18.

Links

Crossrefs

Cf. A000796, A096567, A276992, A361434.

Programs

  • PARI
    \\ See Links section.
Showing 1-8 of 8 results.

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

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