A330084 a(n) is the smallest k > 0 such that n occurs immediately after the decimal point in the decimal expansion of k*Pi.

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

Offset: 0

Author

Felix Fröhlich, Dec 01 2019

Keywords

• nonn
• base

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.

From A266242, only 36 appears in this sequence. - Rémy Sigrist, Dec 01 2019

Examples

			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.
		

Crossrefs

Cf. A000796, A039916, A266242.

Programs

Mathematica

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 *)

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)))

Formula

a(n) = 1 iff n belongs to A039916. - Rémy Sigrist, Dec 01 2019