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

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

Offset

1,1

Links

Table of n, a(n) for n=1..9.

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

Crossrefs

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

Sequence in context: A057583 A129788 A170938 * A338310 A254404 A254403

Adjacent sequences: A003681 A003682 A003683 * A003685 A003686 A003687

Keyword

nonn,fini,full,base,easy,nice

Author

Harvey P. Dale and Jud McCranie

Extensions

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

Status

approved