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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.
0
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
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
KEYWORD
nonn,base
AUTHOR
Ryan Brooks, May 10 2020
STATUS
approved