A307582 Position of the first occurrence of (0, 1, ..., n-1) in the digits of Pi written in base n.

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

Offset

2,1

Comments

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.

Links

Table of n, a(n) for n=2..9.

Formula

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

Example

Pi written in base 2 is 11.001...[2], so the first "01" occurs at position a(2) = 2.
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.
Pi written in base 4 is 3.02100333...[4]; the string of digits "0123" does not occur until position a(4) = 188.

Prog

(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.

Crossrefs

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

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

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

Sequence in context: A173240 A042359 A015174 * A125610 A247028 A333740

Adjacent sequences: A307579 A307580 A307581 * A307583 A307584 A307585

Keyword

nonn,base,more

Author

M. F. Hasler, Apr 15 2019

Extensions

a(7)-a(9) from Chai Wah Wu, Apr 07 2020

Status

approved