A078604 -id:A078604 - 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

A089281 Smallest prime factor of floor(Pi*10^n).

Original entry on oeis.org

3, 31, 2, 3, 5, 314159, 2, 2, 3, 3, 5, 2, 13, 163, 43, 13, 2, 317213509, 2, 2, 2, 2, 2, 2, 83, 41, 2, 3, 2, 3, 3, 5, 2, 2, 2, 2, 2, 31415926535897932384626433832795028841, 13, 59, 3, 2, 3, 3, 3, 3, 3, 31, 3, 1657, 2, 3, 2, 2, 2, 29, 13, 2, 3, 2

Offset: 0

Reinhard Zumkeller, Oct 30 2003

nonn

			n = 10: floor(Pi*10^10) = 31415926535 = 5*7*31*28954771: a(10) = 5.

Tyler Busby, Table of n, a(n) for n = 0..572 (terms 0..59 from Ray Chandler, terms 60..100 from Ryan Moore)

Cf. A078604, A000796 (decimals of Pi), A020639 (smallest prime fector), A011545 (numbers made from inital digits of Pi), A060421 (1 + indices of primes in this sequence).

a[n_] := FactorInteger[IntegerPart[Pi*10^n]][[1, 1]];
Table[a[n], {n, 0, 59}]  (* Peter Luschny, Mar 15 2024 *)

a(n) = factor(floor(Pi*10^n))[1, 1]; \\ Michel Marcus, Dec 28 2013

A089281(n)={localprec(n+3); factor(Pi\10^-n)[1, 1]} \\ M. F. Hasler, Mar 15 2024

a(n) = A020639(A011545(n)).

a(n) is prime (<=> in A000040) iff n+1 is in A060421. - M. F. Hasler, Mar 15 2024

More terms from Ray Chandler, Oct 30 2003

More terms from Ryan Moore, Dec 27 2013

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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A089281 Smallest prime factor of floor(Pi*10^n).

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