A333422 Factorial base emirps: prime numbers whose factorial base reversal is a different prime.

29, 37, 137, 181, 733, 743, 769, 977, 1013, 1031, 1033, 1049, 5107, 5119, 5171, 5179, 5233, 5273, 5297, 5323, 5387, 5393, 5399, 5407, 5437, 5441, 5449, 5471, 5477, 5483, 6571, 6607, 6689, 6691, 6709, 6719, 6733, 6763, 6803, 6823, 6829, 6907, 6947, 6949, 40343

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Wikipedia, Factorial number system.

Index entries for sequences related to factorial base representation.

Example

29 is a term since it is a prime number and its representation in factorial base is 1021, whose reversal, 1201, is the factorial base representation of another prime number, 37.

Mathematica

max = 8; bases = Range[max, 2, -1]; nmax = max! - 1; emirpQ[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n, MixedRadix[bases]]}, r = Reverse @ d; IntegerDigits[(m = FromDigits[r, MixedRadix[bases]]), MixedRadix[bases]] == r && m != n && PrimeQ[m]]; Select[Range[nmax], emirpQ]

Crossrefs

Cf. A007623, A046807, A108731, A333421.

Cf. A006567, A080790.

Sequence in context: A341174 A167470 A152865 * A108272 A121999 A069530

Adjacent sequences: A333419 A333420 A333421 * A333423 A333424 A333425

Keyword

nonn,base

Author

Amiram Eldar, Mar 20 2020

Status

approved