A089290 -id:A089290 - 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

A046974 Partial sums of digits of decimal expansion of Pi.

Original entry on oeis.org

3, 4, 8, 9, 14, 23, 25, 31, 36, 39, 44, 52, 61, 68, 77, 80, 82, 85, 93, 97, 103, 105, 111, 115, 118, 121, 129, 132, 134, 141, 150, 155, 155, 157, 165, 173, 177, 178, 187, 194, 195, 201, 210, 213, 222, 231, 234, 241, 246, 247, 247, 252, 260, 262

Offset: 0

N. J. A. Sloane

a(n) = A007953(A011545(n)). - Reinhard Zumkeller, Oct 30 2003
The partial sums to 10^k, k>=0: 4, 44, 480, 4479, 44897, 449336, 4499937, 45002885, 449989731, .... - Robert G. Wilson v, Sep 16 2007
If the sequence were to start with an initial term a(0) = 0, its first differences would reproduce the complete sequence of digits of Pi. - M. F. Hasler, Jan 19 2015

Mital Ashok, Table of n, a(n) for n = 0..999

Cf. A000796, A089290.

Rest@ FoldList[ Plus, 0, First@ RealDigits[Pi, 10, 58]] (* Robert G. Wilson v, Sep 16 2007 *)
Accumulate[RealDigits[Pi,10,60][[1]]] (* Harvey P. Dale, Mar 11 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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