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.

A160045 Continued fraction for Pi^Pi^Pi A073234.

Original entry on oeis.org

1340164183006357435, 3, 2, 1, 3, 4, 1, 1, 5, 1, 1, 1, 4, 14, 1, 2, 5, 2, 3, 1, 2, 1, 50, 785, 1, 1, 2, 34, 1, 2, 1, 3, 1, 3, 3, 1, 1, 1, 2, 2, 5, 3, 9, 1, 1, 1, 1, 1, 1, 8, 13, 2, 11, 444, 3, 1, 2, 86, 1, 25, 4, 2, 25, 18, 2, 1, 192, 1, 4, 1, 5, 3, 14, 4, 15, 2, 3, 8, 4, 2, 36, 1, 1, 2, 1, 1, 1, 1
Offset: 0

Views

Author

Harry J. Smith, May 01 2009

Keywords

Comments

Pi^Pi^Pi = 1340164183006357435.2974491296401314150993749745734992377879...

Examples

			Pi^Pi^Pi = 1340164183006357435 + 1/(3 + 1/(2 + 1/(1 + 1/(3 + ...)))).

Links

Crossrefs

Cf. A073234 Decimal expansion of Pi^Pi^Pi.

Programs

  • Mathematica
    ContinuedFraction[Pi^Pi^Pi,90] (* Harvey P. Dale, Sep 10 2014 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^Pi^Pi); for (n=1, 20001, write("b160045.txt", n-1, " ", x[n])); }

A073233 Decimal expansion of Pi^Pi.

Original entry on oeis.org

3, 6, 4, 6, 2, 1, 5, 9, 6, 0, 7, 2, 0, 7, 9, 1, 1, 7, 7, 0, 9, 9, 0, 8, 2, 6, 0, 2, 2, 6, 9, 2, 1, 2, 3, 6, 6, 6, 3, 6, 5, 5, 0, 8, 4, 0, 2, 2, 2, 8, 8, 1, 8, 7, 3, 8, 7, 0, 9, 3, 3, 5, 9, 2, 2, 9, 3, 4, 0, 7, 4, 3, 6, 8, 8, 8, 1, 6, 9, 9, 9, 0, 4, 6, 2, 0, 0, 7, 9, 8, 7, 5, 7, 0, 6, 7, 7, 4, 8, 5, 4, 3, 6, 8, 1
Offset: 2

Views

Author

Rick L. Shepherd, Jul 21 2002

Keywords

Comments

A weak form of Schanuel's Conjecture implies that Pi^Pi is transcendental--see Marques and Sondow (2012).

Examples

			36.4621596072079117709908260226...

Links

Crossrefs

Cf. A000796 (Pi), A073234 (Pi^Pi^Pi), A073237 (ceil(Pi^Pi^...^Pi), n Pi's), A073238 (Pi^(1/Pi)), A073239 ((1/Pi)^Pi), A073240 ((1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073236 (Pi analog of A004002).
Cf. A073226 (e^e).
Cf. A049006 (i^i), A116186 (real part of i^i^i).
Cf. A194555 (real part of i^e^Pi).

Programs

  • Mathematica
    RealDigits[N[Pi^Pi,200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)
  • PARI
    Pi^Pi
  • PARI
    { default(realprecision, 20080); x=Pi^Pi/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b073233.txt", n, " ", d)); } \\ Harry J. Smith, Apr 30 2009

A202955 Decimal expansion of Pi^Pi^Pi^Pi.

Original entry on oeis.org

9, 0, 8, 0, 2, 2, 2, 4, 5, 5, 3, 9, 0, 6, 1, 7, 7, 6, 9, 7, 2, 3, 9, 3, 1, 7, 1, 3, 2, 8, 4, 2, 8, 7, 7, 4, 6, 5, 1, 6, 0, 4, 6, 3, 5, 8, 1, 3, 1, 8, 9, 7, 3, 5, 9, 9, 4, 6, 9, 3, 5, 9, 2, 6, 3, 3, 6, 8, 4, 5, 1, 9, 9, 0, 5, 8, 1, 5, 3, 6, 0, 9, 5, 6, 8, 6, 6, 7, 6, 7, 2, 6, 0, 1, 7, 6, 8, 6, 3, 1, 3, 6, 9, 4, 2, 0, 9, 8, 3, 7, 4, 4, 2, 6, 5, 5
Offset: 666262452970848504

Views

Author

M. F. Hasler, Dec 26 2011

Keywords

Comments

The offset equals the floor(Pi^Pi^Pi*Log_10(Pi))+1. - Robert G. Wilson v, Mar 13 2014
Whether this number is an integer or not is an open question. It is also an open question whether Pi^Pi^Pi^...^Pi^Pi n times is an integer for any natural n > 4. - Eliora Ben-Gurion, Nov 17 2019

Examples

			9.080222455390617769723931713284287746516046358131897359946935926336845199... *10^666262452970848503

Crossrefs

Cf. A073236, A085667, A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073235 ((Pi^Pi)^Pi), A202953 ((Pi^Pi)^(Pi^Pi)).

Programs

  • Mathematica
    nbrdgt = 105; f[base_, exp_] := RealDigits[ 10^FractionalPart[ N[exp*Log10[base], nbrdgt + Floor[Log10[exp]] + 2]], 10, nbrdgt][[1]]; f[Pi, Pi^Pi^Pi] (* Robert G. Wilson v, Mar 13 2014 *)
  • PARI
    LP(a,b)=[10^frac(a=log(a)/log(10)*b),a\1] /* returns [m,e] such that a^b = m*10^e */
LP(Pi,Pi^Pi^Pi)

Formula

A000796^A073234.

A073236 Pi^Pi^...^Pi (n times) rounded to nearest integer.

Original entry on oeis.org

1, 3, 36, 1340164183006357435
Offset: 0

Views

Author

Rick L. Shepherd, Jul 25 2002

Keywords

Comments

Decimal expansions (before rounding) of Pi (A000796), Pi^Pi (A073233) and Pi^Pi^Pi (A073234) correspond to a(1), a(2) and a(3), respectively. All four terms are equivalent if floor is used instead of round. See A073237 for same sequence but using ceiling. This sequence is the analog of A004002, which deals with e.
a(4) has 666262452970848504 digits. - Mateusz Winiarski, Mar 23 2020; corrected by Martin Renner, Aug 23 2023

Crossrefs

Cf. A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073237 (Ceiling of Pi^Pi^...^Pi, n times), A004002 (Benford numbers).

Programs

  • Maple
    p:= n-> `if`(n=0, 1, Pi^p(n-1)):
a:= n-> round(p(n)):
seq(a(n), n=0..3);  # Alois P. Heinz, Jul 20 2024
  • Mathematica
    Round[NestList[Power[Pi, #] &, 1, 3]] (* Alonso del Arte, Jul 02 2014 *)
  • PARI
    p=0; for(n=0,3, p=Pi^p; print1(round(p),",")) \\ n = 4 produces too large an exponent for PARI.

Formula

a(n) = round(Pi^Pi^...^Pi), where Pi occurs n times, a(0) = 1 (=Pi^0).

A073241 Decimal expansion of (1/Pi)^(1/Pi)^(1/Pi).

Original entry on oeis.org

4, 5, 1, 5, 0, 8, 3, 4, 5, 5, 3, 6, 5, 7, 2, 8, 0, 5, 2, 2, 1, 9, 9, 3, 8, 1, 8, 0, 4, 4, 7, 3, 4, 0, 3, 6, 5, 4, 0, 9, 0, 2, 8, 0, 2, 6, 4, 5, 9, 7, 9, 7, 0, 5, 1, 8, 5, 4, 4, 2, 7, 3, 0, 0, 4, 1, 2, 5, 2, 6, 6, 9, 2, 7, 8, 9, 4, 8, 3, 4, 8, 2, 7, 7, 2, 5, 5, 0, 6, 0, 0, 3, 5, 5, 8, 4, 3, 1, 0, 8, 9, 3, 0, 8
Offset: 0

Views

Author

Rick L. Shepherd, Jul 27 2002

Keywords

Examples

			0.45150834553657280522199381804...

Crossrefs

Cf. A000796 (Pi), A049541 (1/Pi), A073240 ((1/Pi)^(1/Pi)), A073243 (limit of (1/Pi)^(1/Pi)^...^(1/Pi)), A073242 (((1/Pi)^(1/Pi))^(1/Pi)), A073234 (Pi^Pi^Pi).

Programs

  • Mathematica
    With[{c=1/Pi},RealDigits[c^c^c,10,120][[1]]] (* Harvey P. Dale, Mar 10 2015 *)
  • PARI
    (1/Pi)^(1/Pi)^(1/Pi)

A073235 Decimal expansion of (Pi^Pi)^Pi.

Original entry on oeis.org

8, 0, 6, 6, 2, 6, 6, 5, 9, 3, 8, 5, 5, 4, 5, 9, 6, 7, 3, 8, 4, 9, 8, 3, 6, 0, 1, 8, 9, 7, 7, 4, 6, 6, 8, 0, 7, 1, 9, 3, 6, 0, 0, 6, 8, 0, 5, 2, 5, 1, 4, 9, 6, 0, 5, 9, 9, 5, 0, 4, 7, 7, 0, 8, 9, 3, 0, 1, 4, 5, 9, 0, 1, 3, 1, 1, 5, 4, 9, 8, 4, 4, 3, 6, 1, 6, 3, 0, 1, 5, 8, 4, 0, 3, 9, 0, 0, 8, 2, 6, 1, 3, 2, 6, 9
Offset: 5

Views

Author

Rick L. Shepherd, Jul 25 2002

Keywords

Examples

			80662.6659385545967384983601897...

Crossrefs

Cf. A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073241 ((1/Pi)^(1/Pi)^(1/Pi)), A073242 (((1/Pi)^(1/Pi))^(1/Pi)).

Programs

  • Mathematica
    RealDigits[(Pi^Pi)^Pi, 10, 105][[1]] (* Alonso del Arte, Jul 03 2012 *)
  • PARI
    (Pi^Pi)^Pi

A073237 a(n) = ceiling(Pi^Pi^...^Pi), where Pi appears n times.

Original entry on oeis.org

1, 4, 37, 1340164183006357436
Offset: 0

Views

Author

Rick L. Shepherd, Jul 25 2002

Keywords

Comments

Decimal expansions (before taking ceiling) of Pi (A000796), Pi^Pi (A073233) and Pi^Pi^Pi (A073234) correspond to a(1), a(2) and a(3), respectively. See A073236 for same sequence rounded to nearest integer. This sequence is similar to A004002, which deals with e (but rounds).
a(4) has 666262452970848504 digits. - Martin Renner, Aug 19 2023

Crossrefs

Cf. A000796 (Pi), A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073236 (Pi^Pi^...^Pi, n times, rounded), A004002 (Benford numbers), A056072 (similar to A004002 but takes floor).

Programs

  • Maple
    p:= n-> `if`(n=0, 1, Pi^p(n-1)):
a:= n-> ceil(p(n)):
seq(a(n), n=0..3);  # Alois P. Heinz, Jul 20 2024
  • PARI
    p=0; for(n=0,3, p=Pi^p; print1(ceil(p),",")) \\ n=4 produces too large an exponent for PARI.

Formula

a(n) = ceiling(Pi^Pi^...^Pi), where Pi occurs n times, a(0) = 1 (=Pi^0).

A073242 Decimal expansion of ((1/Pi)^(1/Pi))^(1/Pi).

Original entry on oeis.org

8, 9, 0, 4, 8, 8, 2, 3, 5, 9, 2, 0, 3, 2, 7, 0, 6, 7, 0, 9, 1, 5, 2, 8, 6, 6, 4, 5, 6, 9, 4, 4, 2, 6, 7, 5, 5, 8, 4, 3, 5, 7, 6, 1, 7, 5, 8, 0, 0, 3, 9, 8, 3, 4, 3, 9, 4, 1, 4, 7, 3, 7, 1, 3, 0, 2, 4, 6, 6, 7, 6, 7, 9, 5, 2, 2, 3, 8, 4, 5, 5, 6, 9, 2, 0, 5, 6, 7, 8, 9, 3, 5, 9, 7, 5, 4, 9, 7, 4, 1, 5, 6, 9, 0
Offset: 0

Views

Author

Rick L. Shepherd, Jul 28 2002

Keywords

Examples

			0.89048823592032706709152866456...

Crossrefs

Cf. A000796 (Pi), A049541 (1/Pi), A073240 ((1/Pi)^(1/Pi)), A073241 ((1/Pi)^(1/Pi)^(1/Pi)), A073235 ((Pi^Pi)^Pi), A073234 (Pi^Pi^Pi).

Programs

  • Mathematica
    RealDigits[ N[(1/Pi^(1/Pi))^(1/Pi), 110]][[1]]
  • PARI
    \\ This shorter statement is equivalent to ((1/Pi)^(1/Pi))^(1/Pi): Pi^(-Pi^-2)

A202953 Decimal expansion of x^x with x=Pi^Pi.

Original entry on oeis.org

8, 8, 7, 4, 5, 5, 1, 7, 2, 1, 8, 3, 1, 2, 4, 2, 9, 5, 8, 7, 4, 6, 3, 1, 4, 5, 5, 2, 2, 5, 4, 3, 4, 6, 0, 2, 6, 8, 8, 4, 1, 2, 8, 6, 6, 7, 6, 5, 4, 6, 6, 1, 2, 5, 0, 0, 5, 1, 5, 8, 8, 5, 4, 8, 4, 2, 8, 0, 1, 2, 9, 0, 2, 0, 5, 5, 6, 3, 7, 8, 1, 8, 9, 4, 7, 9, 3, 4, 2, 7, 0, 2, 1, 6, 5, 3, 4, 3, 3, 8
Offset: 57

Views

Author

M. F. Hasler, Dec 26 2011

Keywords

Examples

			887455172183124295874631455225434602688412866765466125005.158854842801290205563781894793427...

Crossrefs

Cf. A073233 (Pi^Pi), A073234 (Pi^Pi^Pi), A073235 ((Pi^Pi)^Pi), A202949 ((e^e)^(e^e)).

Programs

  • Mathematica
    With[{x=Pi^Pi},RealDigits[x^x,10,120][[1]]] (* Harvey P. Dale, Dec 31 2011 *)
  • PARI
    p(x)=x^x /* then type p(p(Pi)) */
Showing 1-9 of 9 results.

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

Content is available under The OEIS End-User License Agreement.