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

61, 62, 5471, 5472, 7116, 8669, 12769, 16546, 18806, 18960, 22260, 23573, 26400, 29094, 29383, 30026, 31121, 36106, 36223, 46432, 53222, 53655, 54014, 56108, 56630, 56762, 59717, 66868, 69532, 70815, 71597, 73937, 74181, 88937, 91918, 106693, 107810, 109174

Offset

1,1

Comments

It is natural to conjecture that a(n) ~ 1562500n/567. - Charles R Greathouse IV, May 22 2015

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

a(n) = A280183(n) + 1. - Bobby Jacobs, Jan 03 2017

Example

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.

Mathematica

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 *)

Prog

(PARI)
default(realprecision, 50080);
infix(v, a, b) = {my(i, s=[]); for(i=a, b, s=concat(s, v[i])); s}
panpi(m) = {
  L=List(); p=Pi; for(n=1, 50000, d=floor(p); p=(p-d)*10; listput(L, d)); v=Vec(L);
  s=[]; for(k=1, #v-m+1, in=infix(v, k, k+m-1); if(#in==#vecsort(in, , 8), s=concat(s, k))); s
}
panpi(10)

Crossrefs

Cf. A000796, A258158, A280182, A280183.

Sequence in context: A258158 A364715 A042859 * A114085 A195378 A260561

Adjacent sequences: A258154 A258155 A258156 * A258158 A258159 A258160

Keyword

nonn,base

Author

Colin Barker, May 22 2015

Extensions

a(21)-a(38) from Giovanni Resta, May 22 2015

Status

approved