

A330084


a(n) is the smallest k > 0 such that n occurs immediately after the decimal point in the decimal expansion of k*Pi.


0



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, 23, 16, 9, 2, 108, 94, 87, 80, 73, 66, 59, 52, 45, 31, 24, 17, 10, 3, 109, 102, 95, 81, 74, 67, 60, 53, 46, 39, 25, 18, 11, 4, 110, 103, 96, 89, 75, 68, 61, 54, 47, 40
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

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.


LINKS



FORMULA



EXAMPLE

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.


MATHEMATICA

a[n_]:=(k=1; While[Floor[(Pi*kFloor[Pi*k])*10^Length[IntegerDigits[n]]]!=n, k++]; Return[k]); Table[a[n], {n, 0, 67}] (* Joshua Oliver, Dec 01 2019 *)


PROG

(PARI) pidigits(multipl, len) = floor((Pi*multipl  floor(Pi*multipl)) * 10^len)
a(n) = for(k=1, oo, if(pidigits(k, #Str(n))==n, return(k)))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



