A316478 Number of base-n digits of Pi that must be read so as to encounter at least one of each digit, 0..n-1.

3, 6, 4, 9, 15, 11, 15, 21, 33, 25, 23, 24, 39, 50, 82, 35, 35, 70, 88, 77, 78, 80, 118, 108, 84, 72, 146, 183, 159, 106, 144, 141, 211, 113, 119, 138, 148, 128, 131, 243, 183, 242, 232, 221, 160, 188, 123, 174, 298, 265, 192, 260, 363, 227, 207, 246, 438, 328

Offset

2,1

Comments

The a(n)-th digit (expressed in base 10) of the base-n expansion of Pi is A316477(n).

Links

Jon E. Schoenfield, Table of n, a(n) for n = 2..3000

Example

The decimal (i.e., base-10) expansion of Pi is
  3.14159265358979323846264338327950...
in which each of the digits 1..9 appears before the first appearance of a digit 0 (= A316477(10)) as the 33rd digit, so a(10) = 33.
Using the characters a..f to represent 10..15, the hexadecimal (i.e., base-16) expansion of Pi is
  3.243f6a8885a308d313198a2e03707344a4093822299f31d0
    082efa98ec4e6c89452821e638d01377b...
in which each of the digits 0..a and c..f appears before the first appearance of a digit b_16 (= 11_10 = A316477(16)) as the 82nd digit, so a(16) = 82.

Mathematica

a[n_] := Block[{r, k=2}, While[n > Length@ Union[r = RealDigits[Pi, n, k n][[1]]], k++]; Max@ Flatten[Position[r, #, 1, 1] & /@ Range[0, n-1]]]; Array[a, 58, 2] (* Giovanni Resta, Jul 08 2018 *)

Crossrefs

Cf. A316477 (Last digit to appear in the base-n expansion of Pi).

Expansion of Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9), A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).

Sequence in context: A321773 A083349 A065230 * A242224 A294671 A275985

Adjacent sequences: A316475 A316476 A316477 * A316479 A316480 A316481

Keyword

nonn,base

Author

Jon E. Schoenfield, Jul 08 2018

Status

approved