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 A037057 #14 Jul 21 2025 00:22:00
%S A037057 3,2,223,2221,22229,1222229,20222227,22222223,222222227,20222222221,
%T A037057 22222222223,2122222222229,21222222222221,22222222222229,
%U A037057 222222222222227,21222222222222221,202222222222222229,222222222222222221,22222202222222222221,220222222222222222229,2202222222222222222229
%N A037057 Smallest prime containing exactly n 2's.
%C A037057 For n > 1, the last digit cannot be 2, so a(n) has at least n+1 digits. The probability is big that none of [10^n/9]*20 + {1,3,7,9} is prime, in which case a(n) must have at least n+2 digits. This is the most frequent case. We can even conjecture that for all n > 1, a(n) equals [10^(n+1)/9]*20 + b with 1 <= b <= 9 and one of the (first) digits 2 replaced by 0 or 1. - _M. F. Hasler_, Feb 22 2016
%H A037057 M. F. Hasler, <a href="/A037057/b037057.txt">Table of n, a(n) for n = 0..200</a>
%F A037057 a(n) = prime(A037056(n)). - _Amiram Eldar_, Jul 21 2025
%t A037057 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, 2], {n, 1, 18}]
%o A037057 (PARI) A037057(n)={my(p,t=10^(n+1)\9*20); n>1 && forvec(v=[[-1,n],[-2,-1]],nextprime(p=t+10^(n-v[1])*v[2])-p<10 && return(nextprime(p)));3-n} \\ _M. F. Hasler_, Feb 22 2016
%Y A037057 Cf. A065585, A037056, A034388, A036507-A036536.
%Y A037057 Cf. A037053, A037055, A037059, A037061, A037063, A037065, A037067, A037069, A037071.
%K A037057 nonn,base
%O A037057 0,1
%A A037057 _Patrick De Geest_, Jan 04 1999
%E A037057 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
%E A037057 More terms and a(0) = 3 from _M. F. Hasler_, Feb 22 2016