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.

A032445 Number the digits of the decimal expansion of Pi: 3 is the first, 1 is the second, 4 is the third and so on; a(n) gives the starting position of the first occurrence of n.

Original entry on oeis.org

33, 2, 7, 1, 3, 5, 8, 14, 12, 6, 50, 95, 149, 111, 2, 4, 41, 96, 425, 38, 54, 94, 136, 17, 293, 90, 7, 29, 34, 187, 65, 1, 16, 25, 87, 10, 286, 47, 18, 44, 71, 3, 93, 24, 60, 61, 20, 120, 88, 58, 32, 49, 173, 9, 192, 131, 211, 405, 11, 5, 128, 220, 21, 313, 23, 8, 118, 99, 606
Offset: 0

Views

Author

Jeff Burch, Paul Simon (paulsimn(AT)microtec.net)

Keywords

Comments

See A176341 for a variant counting positions starting with 0, and A232013 for a sequence based on iterations of A176341. - M. F. Hasler, Nov 16 2013

Examples

			a(10) = 50 because the first "10" in the decimal expansion of Pi occurs at digits 50 and 51: 31415926535897932384626433832795028841971693993751058209749445923...

Links

Crossrefs

Cf. A000796 (decimal expansion of Pi).
Cf. A080597 (terms from the decimal expansion of Pi which include every combination of n digits as consecutive subsequences).
Cf. A032510 (last string seen when scanning the decimal expansion of Pi until all n-digit strings have been seen).
Cf. A064467 (primes in Pi).

Programs

  • Mathematica
    p = ToString[FromDigits[RealDigits[N[Pi, 10^4]][[1]]]]; Do[Print[StringPosition[p, ToString[n]][[1]][[1]]], {n, 1, 100}]
With[{pi=RealDigits[Pi,10,1000][[1]]},Transpose[Flatten[Table[ SequencePosition[ pi,IntegerDigits[n],1],{n,0,70}],1]][[1]]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Dec 01 2015 *)
  • PARI
    A032445(n)=my(L=#Str(n)); n=Mod(n, 10^L); for(k=L-1, 9e9, Pi\.1^k-n||return(k+2-L)) \\ Make sure to use sufficient realprecision, e.g. via \p999. - M. F. Hasler, Nov 16 2013

Formula

a(n) = A176341(n)+1. - M. F. Hasler, Nov 16 2013

Extensions

More terms from Simon Plouffe. Corrected by Michael Esposito and Michelle Vella (michael_esposito(AT)oz.sas.com).
More terms from Robert G. Wilson v, Oct 04 2001

A036906 Scan decimal expansion of zeta(3) until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

Original entry on oeis.org

23, 457, 7839, 83054, 1256587, 13881136, 166670757
Offset: 1

Views

Author

Michael Kleber

Keywords

Links

Crossrefs

Cf. A002117 (decimal expansion of zeta(3)).
Cf. A036902 (last n-digit string seen when scanning the decimal digits of zeta(3)).
Cf. A032510, A036900-A036905.

Extensions

a(7) = 166670757 from Eric W. Weisstein, Sep 17 2013

A080597 Number of terms from the decimal expansion of Pi (A000796) which include every combination of n digits as consecutive subsequences.

Original entry on oeis.org

33, 607, 8556, 99850, 1369565, 14118313, 166100507, 1816743913, 22445207407, 241641121049, 2512258603208
Offset: 1

Views

Author

Martin Hasch (martin(AT)mathematik.uni-ulm.de), Feb 23 2003

Keywords

Examples

			a(2) = 607 because the first 607 digits of Pi contain every conceivable 2-digit subsequence but the first 606 digits do not. The combination (6, 8) appears as 606th and 607th term in A000796.

Links

Crossrefs

Cf. A000796 (decimal expansion of Pi).
Cf. A036903 (= a(n) - 1).
Cf. A032510 (last digit string when scanning the decimal expansion of Pi for all n-digit strings).

Formula

a(n) = A036903(n) + 1. - Eric W. Weisstein, Sep 11 2013

Extensions

a(7)-a(8) from Piotr Idzik, Nov 01 2011
a(9)-a(11) from A036903(n) + 1 by Eric W. Weisstein, Sep 11 2013

A036903 Scan decimal expansion of Pi until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

Original entry on oeis.org

32, 606, 8555, 99849, 1369564, 14118312, 166100506, 1816743912, 22445207406, 241641121048, 2512258603207
Offset: 1

Views

Author

Michael Kleber

Keywords

Links

Crossrefs

Cf. A000796 (decimal expansion of Pi).
Cf. A080597 (= a(n) + 1).
Cf. A032445 (starting positions of the first occurrences of n the decimal expansion of Pi).
Cf. A032510 (last n-digit number seen when scanning for all n-digit numbers).
Cf. A036900-A036906.

Formula

a(n) = A080597(n) - 1.

Extensions

a(8)-a(11) from fabrice(AT)bellard.org (Fabrice Bellard), Oct 23 2011

A036905 Scan decimal expansion of log(2) until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

Original entry on oeis.org

22, 444, 7655, 98370, 1107795, 12983306
Offset: 1

Views

Author

Michael Kleber

Keywords

Links

Crossrefs

Cf. A002162 (decimal expansion of log(2)).
Cf. A036901 (last n-digit number encountered in scanning the decimal digits of log(2)).
Cf. A032510, A036900-A036906.

A036901 Scan decimal expansion of log(2) until all n-digit strings have been seen; a(n) is last string seen.

Original entry on oeis.org

2, 98, 604, 1155, 46847, 175403
Offset: 1

Views

Author

Michael Kleber

Keywords

Links

Crossrefs

Cf. A002162 (decimal expansion of log(2)).
Cf. A036905 (number of digits in the decimal expansion of log(2) that must be scanned to see all n-digit strings).
Cf. A032510, A036900-A036906.

A036902 Scan decimal expansion of zeta(3) until all n-digit strings have been seen; a(n) is last string seen.

Original entry on oeis.org

7, 89, 211, 2861, 43983, 292702, 8261623
Offset: 1

Views

Author

Michael Kleber

Keywords

Links

Crossrefs

Cf. A002117 (decimal expansion of zeta(3)).
Cf. A036906 (number of decimal digits of zeta(3) that must be scanned to see all n-digit strings).
Cf. A032510, A036900-A036906.

Extensions

a(7) = 8261623 from Eric W. Weisstein, Sep 17 2013

A036904 Scan decimal expansion of e until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

Original entry on oeis.org

21, 372, 8092, 102128, 1061613, 12108841, 198150341, 1929504534
Offset: 1

Views

Author

Michael Kleber

Keywords

Comments

The digits scanned are {2, 7, 1, 8, 2, 8, ...}, so the initial 2 in 2.71828... is included and counted as the first digit.

Links

Crossrefs

Cf. A001113 (decimal expansion of e).
Cf. A036900 (last number encountered when scanning the decimal expansion of e for all n-digit strings).
Cf. A088576 (starting positions of the first occurrence of n in the decimal expansion of e).
Cf. A032510, A036900-A036906.

Extensions

a(7) from Piotr Idzik, Nov 01 2011
a(8) from Eric W. Weisstein, Sep 11 2013

A332262 Maximum position to start a search within the decimal digits of Pi in order to find all numeric strings with length n.

Original entry on oeis.org

32, 605, 8553, 99846, 1369560, 14118307, 166100500, 1816743905, 22445207398, 241641121039, 2512258603197
Offset: 1

Views

Author

Martin Renner, Feb 25 2020

Keywords

Comments

The minimum position is always 1.

Examples

			a(1) = 32, since 0 appears at the 32nd decimal digit of Pi.
a(2) = 605, since 68 appears at the 605th decimal digit of Pi.
a(3) = 8553, since 483 appears at the 8553rd decimal digit of Pi.

Links

Crossrefs

Cf. A000796, A032445, A032510, A036903, A080597.

Formula

a(n) = A036903(n) - n + 1 = A080597(n) - n.

Extensions

a(9)-a(11) from A080597(n) - n by Jinyuan Wang, Mar 01 2020
Showing 1-9 of 9 results.

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