cp's OEIS Frontend

A201545 Numbers n such that the n-th digit (after the decimal point) in the decimal expansion of Pi are the occurrence of the least significant digit represented by the more significant digits.

%I A201545 #20 Jul 22 2025 16:17:56
%S A201545 47,281,381,399,515,648,918,928,1303,1538,3746,4026,4812,7347,15911,
%T A201545 19129,19191,26709,27249,27959,28299,29820,34009,36089,36989,37169,
%U A201545 38989,39700,39710,39720,39869,41970,42170,43950,44627,51686,52486,52526,52836,54639,54769
%N A201545 Numbers n such that the n-th digit (after the decimal point) in the decimal expansion of Pi are the occurrence of the least significant digit represented by the more significant digits.
%C A201545 The 47th digit after the decimal point in the expansion of Pi (A000796, but without the leading 3) is the 4th occurrence of the digit 7; the 281st is the 28th occurrence of the digit 1; etc.
%C A201545 Only individual least significant digits are included. Does not include, for example, 467, which is the beginning position of the 4th occurrence of 67.
%H A201545 Michael S. Branicky, <a href="/A201545/b201545.txt">Table of n, a(n) for n = 1..10000</a>
%H A201545 Dave Andersen, <a href="http://www.angio.net/pi/piquery">Pi-Search Page</a>
%H A201545 Michael S. Branicky, <a href="/A201545/a201545.py.txt">Python program for OEIS A201545</a>
%e A201545 The 399th digit after the decimal point in Pi is the 39th occurrence of the digit 9.
%e A201545 225 is not in the sequence, as the 225th digit is 5, but this is the 23rd occurrence of the digit 5 in the expansion of pi, not the 22nd.
%p A201545 Digits := 4000 ;
%p A201545 pdg := proc(n)
%p A201545         floor(Pi*10^n) mod 10 ;
%p A201545 end proc:
%p A201545 dfreq := Vector(10,0) ;
%p A201545 for n from 1 do
%p A201545         d := pdg(n) ;
%p A201545         dfreq[d+1] := dfreq[d+1]+1 ;
%p A201545         ld := n mod 10 ;
%p A201545         hid := floor(n/10) ;
%p A201545         if dfreq[d+1] = hid and ld = d then
%p A201545                 print(n);
%p A201545         end if;
%p A201545 end do: # _R. J. Mathar_, Dec 16 2011
%Y A201545 Cf. A000796, A057680.
%K A201545 nonn,base
%O A201545 1,1
%A A201545 _Matthew Goers_, Dec 02 2011
%E A201545 a(12) and beyond from _Michael S. Branicky_, Mar 06 2025