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A003684
Number of n-digit reversible primes (or emirps) with distinct digits.
21
4, 8, 22, 84, 402, 1218, 3572, 8218, 11804
OFFSET
1,1
EXAMPLE
13, 17, 31, 37, 71, 73, 79 and 97 are reversible primes (emirps), so a(2)=8.
MATHEMATICA
emrpQ[n_]:=Module[{idn=IntegerDigits[n], rev}, rev=Reverse[idn]; rev!=idn && Max[DigitCount[n]] ==1&&PrimeQ[FromDigits[rev]]]; With[{ems=Select[ Prime[ Range[ 51*10^6]], emrpQ]}, Join[ {4}, Table[Count[ems, _?(IntegerLength[ #] == n&)], {n, 2, 9}]]] (* Harvey P. Dale, Nov 29 2014 *)
PROG
(Python)
from sympy import primerange, isprime
def A003684(n):
return len([p for p in primerange(10**(n-1), 10**n)
if len(set(str(p))) == len(str(p)) and isprime(int(str(p)[::-1]))])
# Chai Wah Wu, Aug 14 2014
KEYWORD
nonn,fini,full,base,easy,nice
EXTENSIONS
Typo in example corrected by David Ritterskamp (dritters(AT)usi.edu), Mar 24 2008
STATUS
approved