

A307583


Position where the last of all n! permutations of { 0 .. n1 } occurs in the digits of Pi written in base n.


3




OFFSET

2,1


COMMENTS

By "permutation of { 0 .. n1 }" we mean a string of n distinct digits. "The last" means the permutation which occurs for the first time later than all other permutations.
Position = k means that the string starts with the digit corresponding to the weight n^k; e.g., the first digit after the decimal point has position 1.


LINKS

Table of n, a(n) for n=2..5.


EXAMPLE

Pi written in base 2 is 11.001...[2], so the first "10" occurs at position 0 (starting with the digit of units) and "01" occurs later at position a(2) = 2.
Pi written in base 3 is 10.010211012...[3], we see that the first permutation of 0..2 to appear is "102", at position 2; then "021" at position 3, then "012" at position 7, then "201" at position 12, then "120" at position 39, and finally "210", the last partition not occurring earlier, at position 82 = a(3).
Pi written in base 4 is 3.02100333...[4]; the first permutation of 0..3 is "3012" at position 0 (starting at units digit '3'), the next distinct permutation to occur is "2031" at position 27 etc.; the last permutation not to occur earlier is "2310" at position 961 = a(4).


PROG

(PARI) A307583(n, x=Pi, m=n^n, S=[])={for(k=n2, oo, #Set(d=digits(x\n^k%m, n)) < n1 && next; #Set(d)==n  vecsort(d)==[1..n1]  next; setsearch(S, d) && next; printf("%d: %d, ", kn+1, Vec(d, n)); S=setunion(S, [d]); #S==n!&&return(kn+1))}


CROSSREFS

Cf. A307581 (first start of any permutation of 0 .. n1 in basen digits of Pi).
Cf. A307582 (first occurrence of "01...(n1)" in digits of Pi written in base n).
Cf. A068987 (occurrence of 123...n in decimal digits of Pi), A121280.
Sequence in context: A343588 A259308 A202965 * A061994 A332584 A197641
Adjacent sequences: A307580 A307581 A307582 * A307584 A307585 A307586


KEYWORD

nonn,base,more


AUTHOR

M. F. Hasler, Apr 15 2019


STATUS

approved



