A099651 For each of the C(10,2) = 45 pairs of decimal digits, record the smallest prime containing only these digits (if one exists); sort.

13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 79, 83, 89, 101, 151, 181, 211, 227, 449, 557, 787

Offset

1,1

Comments

The sequence consists of 24 terms, of which 16 cases < 100.

From 45 combinations of 10 decimal digits only 24 can be prime. All least cases are here.

Links

Table of n, a(n) for n=1..24.

Example

Primes with digits of 8 and 9 are in A020472:{89,8999,89899,89989..}. The smallest = 89 is here.
The 24 digit pairs sorted least to greatest that can be prime are {01, 12, 13, 14, 15, 16, 17, 18, 19, 23, 27, 29, 34, 35, 37, 38, 47, 49, 57, 59, 67, 78, 79, 89}. - Michael De Vlieger, Mar 02 2017

Mathematica

Sort@ Map[Module[{k = 1}, While[! SameQ[Union@ IntegerDigits@ Prime@ k, #], k++]; Prime@ k] &, Function[r, {{0, 1}}~Join~DeleteCases[Union@ Map[Sort, Tuples[Range@ 9, 2]], w_ /; Or[Times @@ Boole@ Map[EvenQ, w] > 0, SameQ @@ w, Times @@ Boole@ Map[Mod[#, 3] == 0 &, w] > 0, SubsetQ[r, w], w == {5, 6}]]]@ Select[Range[2, 9], PowerMod[10, #, #] == 0 &]] (* Michael De Vlieger, Mar 02 2017 *)

Crossrefs

Cf. A020449-A020472, A099756.

Sequence in context: A241059 A040136 A049482 * A156666 A331487 A286042

Adjacent sequences: A099648 A099649 A099650 * A099652 A099653 A099654

Keyword

base,fini,full,nonn

Author

Labos Elemer, Nov 11 2004

Status

approved