A037057 Smallest prime containing exactly n 2's.
3, 2, 223, 2221, 22229, 1222229, 20222227, 22222223, 222222227, 20222222221, 22222222223, 2122222222229, 21222222222221, 22222222222229, 222222222222227, 21222222222222221, 202222222222222229, 222222222222222221, 22222202222222222221, 220222222222222222229, 2202222222222222222229
Offset: 0
Links
- M. F. Hasler, Table of n, a(n) for n = 0..200
Crossrefs
Programs
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Mathematica
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}] -
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
Formula
a(n) = prime(A037056(n)). - Amiram Eldar, Jul 21 2025
Extensions
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003
More terms and a(0) = 3 from M. F. Hasler, Feb 22 2016
Comments