The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #18 Jun 28 2023 12:36:37
%S 29,37,137,181,733,743,769,977,1013,1031,1033,1049,5107,5119,5171,
%T 5179,5233,5273,5297,5323,5387,5393,5399,5407,5437,5441,5449,5471,
%U 5477,5483,6571,6607,6689,6691,6709,6719,6733,6763,6803,6823,6829,6907,6947,6949,40343
%N Factorial base emirps: prime numbers whose factorial base reversal is a different prime.
%H Amiram Eldar, <a href="/A333422/b333422.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e 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.
%t 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]
%Y Cf. A007623, A046807, A108731, A333421.
%Y Cf. A006567, A080790.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Mar 20 2020