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A333422
Factorial base emirps: prime numbers whose factorial base reversal is a different prime.
2
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 20 2020
STATUS
approved