A280183 - OEIS

%I #41 Jul 23 2021 07:23:03

%S 60,61,5470,5471,7115,8668,12768,16545,18805,18959,22259,23572,26399,

%T 29093,29382,30025,31120,36105,36222,46431,53221,53654,54013,56107,

%U 56629,56761,59716,66867,69531,70814,71596,73936,74180,88936,91917,106692,107809,109173

%N Positions of pandigital 10-digit numbers after the decimal point in the decimal expansion of Pi.

%C If the 3 before the decimal point is included as a digit, then the positions are in A258157.

%C From _Eduard Roure Perdices_, Jun 16 2021: (Start)

%C It is conjectured that Pi is a normal number in base 10, which would imply that this sequence is infinite.

%C In the first 10^9 decimal digits of Pi, there are 362577 permutations of {0,...,9}, and this value is close to 362880, the expected number of permutations of {0,...,9} in a list of 10^9 random integers from 0 to 9. (End)

%H Eduard Roure Perdices, <a href="/A280183/b280183.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A258157(n) - 1.

%t final = 10^5; digits = RealDigits[Pi, 10, final][[1]];

%t an = {}; init = 1; While[init + 9 <= final,

%t list = Union[Table[digits[[init + i]], {i, 0, 9}]];

%t If[Length[list] == 10, AppendTo[an, init - 1]];

%t init++;

%t ]; an (* _Eduard Roure Perdices_, Jun 16 2021 *)

%Y Cf. A000796 (Pi), A258157, A280182.

%K nonn,base

%O 1,1

%A _Bobby Jacobs_, Dec 28 2016