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 A037059 #25 Jul 21 2025 00:22:12
%S A037059 2,3,233,2333,23333,313333,3233333,31333333,333233333,3233333333,
%T A037059 23333333333,333313333333,3333333333383,33133333333333,
%U A037059 323333333333333,1333333333333333,23333333333333333,333333133333333333,3333313333333333333,33313333333333333333
%N A037059 Smallest prime containing exactly n 3's.
%C A037059 For almost all n >= 0, a(n) equals [10^(n+1)/3] with one of the (first) digits 3 replaced by a digit 1 or 2. We conjecture that in the few other cases (e.g., for n = 12, 119, ...) the statement holds with some digit 3 replaced by a digit among {4, 5, 7, 8}, except for the special case a(1) = 3. - _M. F. Hasler_, Feb 22 2016
%H A037059 M. F. Hasler, <a href="/A037059/b037059.txt">Table of n, a(n) for n = 0..200</a>; a(1) through a(100) from Harvey P. Dale.
%F A037059 a(n) = prime(A037058(n)). - _Amiram Eldar_, Jul 21 2025
%t A037059 f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[b, {i, 1, n}], {x}]], c = Complement[Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[r ? Infinity, r, p = Permutations[ Join[ Table[ b, {i, 1, n}], {x, y}]]; q = {}; Do[q = Append[q, Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]]]; Table[ f[n, 3], {n, 1, 18}]
%t A037059 Table[Sort[Flatten[Table[Select[FromDigits/@Permutations[Join[{n},PadRight[{},i,3]]], PrimeQ],{n,0,9}]]][[1]],{i,20}] (* _Harvey P. Dale_, Feb 28 2015 *)
%o A037059 (PARI) A037059(n)={if(n==1,3,my(t=10^(n+1)\3); forvec(v=[[-1, n], [-2, -1]], ispseudoprime(p=t+10^(n-v[1])*v[2]) && return(p)); forvec(v=[[0, n], [1, 5]], ispseudoprime(p=t+10^v[1]*v[2]) && return(p)))} \\ _M. F. Hasler_, Feb 22 2016
%Y A037059 Different from A065580.
%Y A037059 Cf. A065586, A065580, A037058, A034388, A036507-A036536.
%Y A037059 Cf. A037053, A037055, A037057, A037061, A037063, A037065, A037067, A037069, A037071.
%K A037059 nonn,base
%O A037059 0,1
%A A037059 _Patrick De Geest_, Jan 04 1999
%E A037059 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
%E A037059 More terms and a(0) = 2 prefixed by _M. F. Hasler_, Feb 22 2016