A089281 -id:A089281 - 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

A078604 Largest prime factor of the integer formed by truncating the decimal expansion of Pi to n places.

Original entry on oeis.org

3, 31, 157, 349, 103, 314159, 392699, 8263, 7853, 9786893, 28954771, 157079632679, 68246533, 4304347, 67649047, 1002742628021, 1170899, 990371647, 14523877, 1186001, 1023100457, 451661057, 1492315939, 381315143078063, 950007203269

Offset: 0

Jason Earls, Dec 09 2002

			a(3) = 157 since 314 = 2*157.

Tyler Busby, Table of n, a(n) for n = 0..200 (terms 0..100 from Ryan Moore, terms 101..169 from Robert G. Wilson)
I. O. Angell, and H. J. Godwin, On Truncatable Primes Math. Comput. 31, 265-267, 1977.
Hisanori Mishima, Decimal expansions of π (n = 0 to 100)
Hisanori Mishima, Decimal expansions of π (n = 101 to 200)
Hisanori Mishima, Decimal expansions of π (n = 201 to 250)
Index entries for sequences related to truncatable primes

Cf. A011545, A006530.

Cf. A089281.

f[n_] := FactorInteger[ IntegerPart[ Pi*10^(n - 1)]][[-1, 1]]; Array[f, 23] (* Robert G. Wilson v, May 30 2015 *)

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

a(n) = A006530(A011545(n)). - Michel Marcus, Dec 28 2013

a(n) = A011545(n) iff n is a term in A060421. - Robert G. Wilson v, May 30 2015

More terms from Ryan Moore, Dec 28 2013

A094875 a(n)=1 if floor(Pi*10^n) is prime, otherwise a(n)=0.

Original entry on oeis.org

1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Frederic E.D. Michaud (famillesmichaud(AT)hotmail.com), Jun 16 2004

nonn

			a(0)=1 because 3 is prime,
a(2)=0 because 314 is divided by 2
a(5)=1 because 314159 is prime
a(13)=0 because 31415926535897 is divided by 163

Cf. A089281, A000796, A010051.

\p 120 a=vector(100);v=1;for(i=1,100,a[i]=isprime(floor(Pi*v));v=v*10)

More terms from Johan Claes, Jun 16 2004

A371224 Least prime factor of the integer formed by the first n decimal digits of Pi, or 0 if that number is prime.

Original entry on oeis.org

0, 0, 2, 3, 5, 0, 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, 0, 13, 59, 3, 2, 3, 3, 3, 3, 3, 31, 3, 1657, 2, 3, 2, 2, 2, 29, 13, 2, 3, 2, 2, 5, 2828293681646068747, 2, 3, 2, 223, 2, 7

Offset: 1

M. F. Hasler, Mar 15 2024

Complementary to the sequences A005042 (primes in the initial digits of Pi) and A060421 which lists numbers N such that the first N digits of Pi form a prime - exactly the indices of zeros in the present sequence.

Cf. A000796 (decimals of Pi), A005042 (primes in A011545), A011545 (integer made of n+1 initial digits of Pi), A060421 (length of A005042(n)), A020639 (smallest prime factor of n), A000040 (primes), A089281 (smallest prime factor of A011545(n)).

a(n, c=Pi)={ if( n>=precision(c), error("insufficient precision"), !ispseudoprime(c\10^-n--), factor(c\.1^n)[1,1], 0)}

a(n) = 0 <=> n is in A060421 <=> A011545(n-1) is in A000040 (primes).
a(n) = A089281(n) = A020639(A011545(n-1)) whenever a(n) is nonzero.
a(n) = 2 <=> A000796(2-n) is even <=> A011545(n-1) is even.

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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A078604 Largest prime factor of the integer formed by truncating the decimal expansion of Pi to n places.

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A094875 a(n)=1 if floor(Pi*10^n) is prime, otherwise a(n)=0.

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A371224 Least prime factor of the integer formed by the first n decimal digits of Pi, or 0 if that number is prime.

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Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula