A003684 Number of n-digit reversible primes (or emirps) with distinct digits.

4, 8, 22, 84, 402, 1218, 3572, 8218, 11804

Offset: 1

Author

Harvey P. Dale and Jud McCranie

Keywords

• nonn
• fini
• full
• base
• easy
• nice

Examples

			13, 17, 31, 37, 71, 73, 79 and 97 are reversible primes (emirps), so a(2)=8.
		

Crossrefs

Cf. A006567, A007628, A046732, A048051, A048052, A048053, A048054, A048895.

Programs

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 *)

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

Extensions

Typo in example corrected by David Ritterskamp (dritters(AT)usi.edu), Mar 24 2008