0,1

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

M. F. Hasler, Table of n, a(n) for n = 0..200; a(1) through a(100) from Harvey P. Dale.

a(n) = prime(A037058(n)). - Amiram Eldar, Jul 21 2025

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}]

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 *)

(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

Different from A065580.

Cf. A065586, A065580, A037058, A034388, A036507-A036536.

Cf. A037053, A037055, A037057, A037061, A037063, A037065, A037067, A037069, A037071.

Sequence in context: A142960 A117324 A355962 * A302398 A087313 A004876

Adjacent sequences: A037056 A037057 A037058 * A037060 A037061 A037062

nonn,base

Patrick De Geest, Jan 04 1999

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003

More terms and a(0) = 2 prefixed by M. F. Hasler, Feb 22 2016

approved