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.

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, 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, 6, 2, 5, 6, 5, 5, 2, 2, 2, 4, 2, 4, 1, 6, 4

Offset

1,1

Comments

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)!).

Links

Table of n, a(n) for n=1..83.

Sean A. Irvine, Java program (github)

Example

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,...

Prog

(PARI)
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)}
{ localprec(10^3); my(t=Pi-3); F(digits(floor(t*10^precision(t)))) } \\ Andrew Howroyd, Aug 10 2020

Crossrefs

Cf. A000796 (Pi). Essentially the same as A104807.

Sequence in context: A085219 A197207 A197805 * A187788 A085072 A077200

Adjacent sequences: A334751 A334752 A334753 * A334755 A334756 A334757

Keyword

nonn,base

Author

Ryan Brooks, May 10 2020

Status

approved