

A331486


Numbers k which are emirps in more bases 1 < b < k than any previous number.


2



2, 5, 7, 11, 13, 17, 23, 29, 31, 41, 43, 53, 67, 73, 79, 97, 113, 127, 157, 193, 223, 269, 277, 311, 379, 421, 431, 467, 487, 563, 613, 647, 743, 907, 937, 977, 1093, 1193, 1249, 1259, 1373, 1483, 1543, 1637, 1667, 1933, 2239, 2393, 2477, 2521, 2857, 2957, 3083
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OFFSET

1,1


COMMENTS

The corresponding numbers of bases are 0, 1, 3, 6, 8, 9, 12, 13, 17, 21, 24, ... (see the link for more values).


LINKS



EXAMPLE

2 is not emirp in any base.
5 is emirp in one base, 3: 5 is 12 in base 3, and 21 in base 3 is 7 which is also a prime.
7 is emirp in 3 bases, 3, 4, and 5.


MATHEMATICA

emirpQ[n_, b_] := n != (rev = FromDigits[Reverse @ IntegerDigits[n, b], b]) && And @@ PrimeQ[{n, rev}];
emirpCount[n_] := Length @ Select[Range[2, n  1], emirpQ[n, #] &];
seq = {}; emax = 1; Do[e1 = emirpCount[n]; If[e1 > emax, emax = e1; AppendTo[seq, n]], {n, 2, 3000}]; seq


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



