cp's OEIS Frontend

A334754 The size of partitions of the decimal digits of Pi, starting directly after the decimal point, such that each partition contains the maximum number of digits possible while also avoiding any repeated digits. A digit must be in a partition if the current partition does not contain the current digit.

%I A334754 #34 Oct 03 2020 02:59:38
%S A334754 2,5,2,4,3,5,3,2,6,2,5,4,1,6,7,2,10,5,5,4,4,5,2,4,6,2,6,5,7,1,5,2,3,4,
%T A334754 3,7,2,2,1,7,5,7,1,3,1,4,3,4,3,3,6,3,7,4,2,5,4,4,4,7,4,3,5,4,5,5,5,4,
%U A334754 6,2,5,6,5,5,2,2,2,4,2,4,1,6,4
%N A334754 The size of partitions of the decimal digits of Pi, starting directly after the decimal point, such that each partition contains the maximum number of digits possible while also avoiding any repeated digits. A digit must be in a partition if the current partition does not contain the current digit.
%C A334754 Assuming digits are random, the expected value for the size of the partitions is 3.66021568 = Sum_{k=1..10} k^2*9!/(10^k*(10-k)!).
%H A334754 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a334/334754.java">Java program</a> (github)
%e A334754 Pi=3.1415926535897932384626433... => ignore lead 3 and partition as such: 0.|14|15926|53|5897|932|38462|643|3... => 2,5,2,4,3,5,3,...
%o A334754 (PARI)
%o A334754 F(v)={my(L=List(), S=Set()); for(i=1, #v, if(setsearch(S, v[i]), listput(L,#S); S=Set()); S=setunion(S,[v[i]])); Vec(L)}
%o A334754 { localprec(10^3); my(t=Pi-3); F(digits(floor(t*10^precision(t)))) } \\ _Andrew Howroyd_, Aug 10 2020
%Y A334754 Cf. A000796 (Pi). Essentially the same as A104807.
%K A334754 nonn,base
%O A334754 1,1
%A A334754 _Ryan Brooks_, May 10 2020