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 A258157 Indices of the start of 10 successive distinct digits in the decimal expansion of Pi. 4

%I

%S 61,62,5471,5472,7116,8669,12769,16546,18806,18960,22260,23573,26400,

%T 29094,29383,30026,31121,36106,36223,46432,53222,53655,54014,56108,

%U 56630,56762,59717,66868,69532,70815,71597,73937,74181,88937,91918,106693,107810,109174

%N Indices of the start of 10 successive distinct digits in the decimal expansion of Pi.

%C It is natural to conjecture that a(n) ~ 1562500n/567. - _Charles R Greathouse IV_, May 22 2015

%H Giovanni Resta, <a href="/A258157/b258157.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A280183(n) + 1. - _Bobby Jacobs_, Jan 03 2017

%e 61 is in the sequence because the 10 digits starting at the 61st digit of Pi are 4, 5, 9, 2, 3, 0, 7, 8, 1, 6.

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

%Y Cf. A000796, A258158, A280182, A280183.

%K nonn,base

%O 1,1

%A _Colin Barker_, May 22 2015

%E a(21)-a(38) from _Giovanni Resta_, May 22 2015

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)