A258158 - OEIS

%I #12 May 22 2015 12:00:28

%S 61,62,63,2007,2008,2187,2188,2402,2814,3312,3313,5013,5471,5472,5473,

%T 6856,7114,7116,7117,7548,7633,7634,7635,7904,8080,8158,8245,8246,

%U 8667,8668,8669,8670,10100,10131,10207,10244,10552,11090,11548,11621,11681,12298

%N Indices of the start of 9 successive distinct digits in the decimal expansion of Pi.

%C It is natural to conjecture that a(n) ~ 156250n/567. - _Charles R Greathouse IV_, May 22 2015

%H Giovanni Resta, <a href="/A258158/b258158.txt">Table of n, a(n) for n = 1..10000</a>

%e 63 is in the sequence because the 9 digits starting at the 63rd digit of Pi are 9, 2, 3, 0, 7, 8, 1, 6, 4.

%t pan[s_, n_]:=Select[Range[Length@s-n+1], Length@ Union@ Take[s, {#, #+n-1}]==n&]; pan[RealDigits[Pi, 10, 10^5][[1]], 9] (* _Giovanni Resta_, May 22 2015 *)

%o (PARI)

%o default(realprecision, 50080);

%o infix(v, a, b) = {my(i, s=[]); for(i=a, b, s=concat(s, v[i])); s}

%o panpi(m) = {

%o   L=List(); p=Pi; for(n=1, 50000, d=floor(p); p=(p-d)*10; listput(L, d)); v=Vec(L);

%o   s=[]; for(k=1, #v-m+1, in=infix(v, k, k+m-1); if(#in==#vecsort(in,,8), s=concat(s, k))); s

%o }

%o panpi(9)

%Y Cf. A000796, A258157.

%K nonn,base

%O 1,1

%A _Colin Barker_, May 22 2015