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

1,1

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

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

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

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

Sequence in context: A228200 A245063 A168033 * A257974 A323782 A020591

Adjacent sequences: A331483 A331484 A331485 * A331487 A331488 A331489

Keyword

nonn,base

Author

Amiram Eldar, Jan 23 2020

Status

approved