This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341046 #35 Jun 26 2021 09:52:43
%S A341046 1,36,106,29486,32876,66317,1360120,22060516,78256779,1151791169,
%T A341046 6701487259,6701487259,1142027682075,2851718461558,91822653867264,
%U A341046 136308121570117,1952799169684491,21208174623389167,842468587426513207,842468587426513207,84383735478118508040
%N A341046 a(n) is the smallest k such that the fractional part of the decimal expansion of k*Pi begins with n zeros.
%H A341046 Jon E. Schoenfield, <a href="/A341046/a341046_1.txt">Magma program</a>
%e A341046 a(0)=1 because Pi*1=3.1415... has 0 zeros at the start of the fractional part of the decimal expansion, and 1 is the smallest positive integer that has this property.
%e A341046 a(1)=36 because Pi*36=113.09733... has 1 zero, and 36 is the smallest positive integer that has this property.
%e A341046 a(2)=106 because Pi*106=333.00882128... has 2 zeros, and 106 is the smallest positive integer that has this property.
%e A341046 From _Jon E. Schoenfield_, Feb 05 2021: (Start)
%e A341046 For each term a(n), the integer part of the corresponding product Pi*a(n) is A341047(n). Terms and their corresponding untruncated products begin as follows:
%e A341046 .
%e A341046 n a(n) Pi*a(n)
%e A341046 -- ------------- ------------------------------
%e A341046 0 1 3.1415926535897...
%e A341046 1 36 113.0973355292325...
%e A341046 2 106 333.0088212805180...
%e A341046 3 29486 92633.0009837486434...
%e A341046 4 32876 103283.0000794180425...
%e A341046 5 66317 208341.0000081143181...
%e A341046 6 1360120 4272943.0000005495794...
%e A341046 7 22060516 69305155.0000000911737...
%e A341046 8 78256779 245850922.0000000061180...
%e A341046 9 1151791169 3618458675.0000000005971...
%e A341046 10 6701487259 21053343141.0000000000017...
%e A341046 11 6701487259 21053343141.0000000000017...
%e A341046 12 1142027682075 3587785776203.0000000000003...
%e A341046 .
%e A341046 a(10) = 6701487259 because no multiple of Pi less than the product 6701487259*Pi = 21053343141.0000000000017... has a fractional part whose first 10 digits after the decimal point are all zeros, but that product does.
%e A341046 Note, however, that that product's 11th digit after the decimal point is also a zero; thus, a(11) = a(10). Presumably, a similar situation occurs infinitely many times; a(n) = a(n-1) at n = 11, 19, 39, 41, 74, 156, 183, 217, 218, 219, 220, 247, .... The consecutive integers 217..220 are in this list because a(220)=a(219)=a(218)=a(217)=a(216).
%e A341046 (End)
%t A341046 A341046[n_] := Module[{m = 1, i = 0}, While[i < n + 1, i = Abs[Floor[Log[10, Abs[FractionalPart[N[Pi*m]]]]]]; m++]; m - 1]; Table[A341046[n], {n, 0, 7}] (* _Robert P. P. McKone_, Feb 04 2021 *)
%Y A341046 Cf. A000796, A341047.
%K A341046 nonn,base
%O A341046 0,2
%A A341046 _Talha Ali_, Feb 04 2021
%E A341046 a(6)-a(8) from _Metin Sariyar_, Feb 04 2021
%E A341046 More terms from _Jon E. Schoenfield_, Feb 05 2021