A037071 - OEIS

%I #14 Feb 23 2016 10:35:16

%S 2,19,199,1999,49999,199999,2999999,19999999,799999999,9199999999,

%T 59999999999,959999999999,9919999999999,59999999999999,

%U 499999999999999,9299999999999999,99919999999999999,994999999999999999,9991999999999999999,29999999999999999999,989999999999999999999

%N Smallest prime containing exactly n 9's.

%C We conjecture that for all n >= 0, a(n) equals [10^(n+1)/9]*9 with one of the (first) digits 9 replaced by a digit among {1, 2, 4, 5, 7, 8}. - _M. F. Hasler_, Feb 22 2016

%H M. F. Hasler, <a href="/A037071/b037071.txt">Table of n, a(n) for n = 0..200</a>

%t 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, 9], {n, 1, 20}]

%o (PARI) A037071(n)={my(t=10^(n+1)\9*9); forvec(v=[[-1, n], [-8, -1]], ispseudoprime(p=t+10^(n-v[1])*v[2]) && return(p));error} \\ _M. F. Hasler_, Feb 22 2016

%Y Cf. A065592, A065582, A037070, A034388, A036507-A036536.

%Y Cf. A037053, A037055, A037057, A037059, A037061, A037063, A037065, A037067, A037069.

%K nonn,base

%O 0,1

%A _Patrick De Geest_, Jan 04 1999

%E More terms from _Vladeta Jovovic_, Jan 10 2002

%E a(0) = 2 prepended by _M. F. Hasler_, Feb 22 2016