A089283 -id:A089283 - cp's OEIS frontend

A011545 a(n) is the integer whose decimal digits are the first n+1 decimal digits of Pi.

3, 31, 314, 3141, 31415, 314159, 3141592, 31415926, 314159265, 3141592653, 31415926535, 314159265358, 3141592653589, 31415926535897, 314159265358979, 3141592653589793, 31415926535897932, 314159265358979323, 3141592653589793238, 31415926535897932384

Offset: 0

N. J. A. Sloane

Number of collisions occurring in a system consisting of an infinitely massive, rigid wall at the origin, a ball with mass m stationary at position x1 > 0, and a ball with mass (10^2n)m at position x2 > x1 and rolling toward the origin, assuming perfectly elastic collisions and no friction. - Richard Holmes, Jun 17 2021

Wolfgang Haken (1977) conjectured that no term of this sequence is a perfect square, and estimated the probability that this conjecture is false to be smaller than 10^-9. - Paolo Xausa, Jul 15 2023

Martin Gardner, Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American Magazine, W. H. Freemand and Company, New York, NY, 1992, pp. 274-275.

Paolo Xausa, Table of n, a(n) for n = 0..100
G. Galperin, Playing pool with π (the number π from a billiard point of view), Regular and Chaotic Dynamics, 8 (2003), 375-394.
Wolfgang Haken, An attempt to understand the four color problem, in Journal of Graph Theory, Vol. 1, Issue 3, 1977, pp. 193-206.
G. Sanderson, Why do colliding blocks compute pi?, a 3Blue1Brown YouTube video, Jan 20 2019.

Cf. A000796 (decimal expansion of Pi), A089281, A078604, A089282, A089283, A089284, A089285, A089286, A089287, A089288, A089289, A046974, A089290.

s=RealDigits[Pi, 10, 30][[1]]; Table[FromDigits[Take[s, n]], {n, Length[s]}]
(* Or: *)
a[n_] := IntegerPart[Pi*10^n]; Table[a[n], {n, 0, 9}] (* Peter Luschny, Mar 15 2024 *)

A011545(n)={localprec(n+3); Pi\10^-n} \\ M. F. Hasler, Mar 15 2024

a(n) = floor(Pi*10^n).

Definition corrected by M. F. Hasler, Mar 15 2024

A089282 Number of distinct prime factors of floor(Pi*10^n), Pi=3.14...

Original entry on oeis.org

1, 1, 2, 2, 3, 1, 2, 3, 5, 3, 4, 2, 3, 3, 3, 3, 5, 2, 6, 5, 4, 6, 7, 6, 3, 4, 8, 3, 4, 6, 4, 6, 7, 2, 4, 4, 6, 1, 5, 2, 4, 5, 3, 5, 4, 6, 5, 3, 7, 3, 5, 5, 3, 6, 7, 5, 4, 5, 4, 6, 5, 7, 3, 5, 4, 6, 5, 5, 3, 4, 7, 8, 6, 6, 6, 5, 5, 6, 8, 5, 5, 4, 7, 7, 5, 6, 4

Offset: 0

Reinhard Zumkeller, Oct 30 2003

nonn

			n=6: floor(Pi*10^6) = 3141592 = 2*2*2*392699: a(6)=2.

Tyler Busby, Table of n, a(n) for n = 0..200

Cf. A001221, A011545, A089283, A000796.

Table[PrimeNu[Floor[Pi 10^n]],{n,0,80}] (* Harvey P. Dale, Dec 19 2022 *)

a(n) = A001221(A011545(n)).

More terms from Ray Chandler, Oct 31 2003

a(81)-a(86) from Tyler Busby, Mar 14 2025

A089287 Sum of all prime factors of floor(Pi*10^n), Pi=3.14....

Original entry on oeis.org

3, 31, 159, 355, 169, 314159, 392705, 10166, 7998, 9787003, 28954814, 157079632681, 68250087, 4349287, 67757089, 1002742628275, 1230791, 1307585156, 14846149, 1296188, 1024025943, 452477425, 1492388104, 381315143079141, 989849547461, 841346597336054869

Offset: 0

Reinhard Zumkeller, Oct 30 2003

nonn

a(n) = A001414(A011545(n)).

			n=6: floor(Pi*10^6)=3141592=2*2*2*392699: a(6)=2+2+2+392699=392705.

Tyler Busby, Table of n, a(n) for n = 0..200

Cf. A089286, A089285, A089283, A000796.

sapf[n_]:=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]; sapf/@ Floor[Pi 10^Range[0,30]] (* Harvey P. Dale, Nov 18 2018 *)

a(23)-a(25) from Tyler Busby, Mar 14 2025

A089284 Number of divisors of floor(Pi*10^n), Pi=3.14...

Original entry on oeis.org

2, 2, 4, 6, 8, 2, 8, 8, 48, 8, 16, 4, 8, 8, 8, 8, 72, 4, 64, 96, 16, 64, 128, 128, 8, 24, 256, 8, 32, 64, 16, 64, 192, 4, 24, 40, 96, 2, 32, 4, 16, 48, 8, 32, 16, 64, 48, 8, 320, 8, 32, 48, 8, 64, 192, 48, 16, 32, 16, 64, 96, 128, 8, 120, 16, 64, 32, 48, 8, 32, 192, 512, 64, 96, 144

Offset: 0

Reinhard Zumkeller, Oct 30 2003

nonn

			For n=4: floor(Pi*10^4)=31415 has divisors: 1,5,61,103,305,515,6283,31415; a(4)=8.

Tyler Busby, Table of n, a(n) for n = 0..200
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
Hisanori Mishima, Decimal expansions of pi (n = 0 to 100, n = 101 to 200, n = 201 to 250).

Cf. A089282, A089283, A000796.

Table[ DivisorSigma[ 0, Floor[ Pi*10^n]], {n, 0, 10}] (* Robert G. Wilson v, Oct 30 2003 *)

A089284(n)=numdiv(Pi\.1^n)  \\ M. F. Hasler, Nov 01 2012

a(n) = A000005(A011545(n)).

More terms from Robert G. Wilson v and Ray Chandler, Oct 30 2003

cp's OEIS Frontend

A011545 a(n) is the integer whose decimal digits are the first n+1 decimal digits of Pi.

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A089282 Number of distinct prime factors of floor(Pi*10^n), Pi=3.14...

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Mathematica

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A089287 Sum of all prime factors of floor(Pi*10^n), Pi=3.14....

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Author

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Comments

Examples

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Crossrefs

Programs

Mathematica

Extensions

A089284 Number of divisors of floor(Pi*10^n), Pi=3.14...

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions