%I #18 Dec 11 2019 02:30:07
%S 36,1,2,24,3,4,12,5,6,7,29,22,15,8,1,100,93,86,79,72,65,58,51,37,30,
%T 23,16,9,2,108,94,87,80,73,66,59,52,45,31,24,17,10,3,109,102,95,81,74,
%U 67,60,53,46,39,25,18,11,4,110,103,96,89,75,68,61,54,47,40
%N a(n) is the smallest k > 0 such that n occurs immediately after the decimal point in the decimal expansion of k*Pi.
%C Any number occurring in this sequence occurs infinitely many times since the smallest such k for a specific n is also the smallest such k for all numbers formed by the concatenation of the initial digits after the decimal point in the decimal expansion of k*Pi.
%C From A266242, only 36 appears in this sequence. - _Rémy Sigrist_, Dec 01 2019
%F a(n) = 1 iff n belongs to A039916. - _Rémy Sigrist_, Dec 01 2019
%e For n = 0: The decimal expansion of 36*Pi starts 113.097335529232... and this is the smallest multiple of Pi where 0 occurs immediately after the decimal point, so a(0) = 36.
%t a[n_]:=(k=1;While[Floor[(Pi*k-Floor[Pi*k])*10^Length[IntegerDigits[n]]]!=n,k++];Return[k]);Table[a[n],{n,0,67}] (* _Joshua Oliver_, Dec 01 2019 *)
%o (PARI) pidigits(multipl, len) = floor((Pi*multipl - floor(Pi*multipl)) * 10^len)
%o a(n) = for(k=1, oo, if(pidigits(k, #Str(n))==n, return(k)))
%Y Cf. A000796, A039916, A266242.
%K nonn,base
%O 0,1
%A _Felix Fröhlich_, Dec 01 2019