A331486 Numbers k which are emirps in more bases 1 < b < k than any previous number.

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

Offset: 1

Author

Amiram Eldar, Jan 23 2020

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..175
• Amiram Eldar, Table of n, a(n), number of bases for n = 1..175

Crossrefs

Cf. A006567, A080790, A087911, A107129, A228768.

Programs

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