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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.
6
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.
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
KEYWORD
base,fini,full,nonn
AUTHOR
Labos Elemer, Nov 11 2004
STATUS
approved