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

0, 2, 1, 4, 2, 2, 6, 5, 0, 9, 2, 8, 6, 10, 11, 11, 12, 6, 4, 7, 4, 14, 15, 20, 22, 20, 22, 16, 29, 22, 7, 25, 30, 26, 14, 18, 16, 38, 32, 23, 28, 7, 9, 19, 4, 0, 16, 42, 21, 17, 34, 41, 39, 11, 38, 32, 28, 48, 27, 1, 27, 12, 56, 30, 20, 61, 66, 63, 54, 67, 25

Offset

2,2

Comments

The number of digits that must be read so as to reach the first appearance of a digit a(n) is A316478(n).

Links

Jon E. Schoenfield, Table of n, a(n) for n = 2..5000

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, so a(10) = 0.
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, so a(16) = 11.

Mathematica

a[n_] := Block[{r, k=2}, While[n > Length@ Union[r = RealDigits[Pi, n, k n][[1]]], k++]; r[[Max@ Flatten[Position[r, #, 1, 1] & /@ Range[0, n-1]]]]]; Array[a, 71, 2] (* Giovanni Resta, Jul 08 2018 *)

Crossrefs

Cf. 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).

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: A343998 A300586 A094571 * A104733 A348676 A201703

Adjacent sequences: A316474 A316475 A316476 * A316478 A316479 A316480

Keyword

nonn,base

Author

Jon E. Schoenfield, Jul 06 2018

Status

approved