%I #12 Apr 07 2020 19:48:49

%S 2,7,188,2264,27931,110808,23489363,97438020

%N Position of the first occurrence of (0, 1, ..., n-1) in the digits of Pi written in base n.

%C Position refers to the digit where there required sequence (0, ..., n-1) starts. Position = k means the digit '0' occurs as digit corresponding to the weight n-^k (and thereafter, the digit '1' will correspond to n^-(k+1) etc): e.g., the first digit after the decimal point has position 1.

%F A307581(n) <= a(n) <= A307583(n).

%e Pi written in base 2 is 11.001...[2], so the first "01" occurs at position a(2) = 2.

%e Pi written in base 3 is 10.010211012...[3], we see that the first occurrence of the string "012" is at position a(3) = 7.

%e Pi written in base 4 is 3.02100333...[4]; the string of digits "0123" does not occur until position a(4) = 188.

%o (PARI) A307582(n,x=Pi,m=Mod(sum(i=1,n-1,i*n^(n-1-i)),n^n))={for(k=oo,x\n^-k==m&&return(k-n+1)) \\ Ensure sufficient precision of the argument x = pi.

%Y Cf. A307581 (first occurrence of any permutation of 0 .. n-1, in base-n digits of Pi).

%Y Cf. A307583 (start of last permutation of {0 .. n-1} not to occur earlier, in base-n digits of Pi).

%Y Cf. A068987 (occurrence of 123...n in decimal digits of Pi), A121280.

%K nonn,base,more

%O 2,1

%A _M. F. Hasler_, Apr 15 2019

%E a(7)-a(9) from _Chai Wah Wu_, Apr 07 2020