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A003684 Number of n-digit reversible primes (or emirps) with distinct digits. 12
4, 8, 22, 84, 402, 1218, 3572, 8218, 11804 (list; graph; refs; listen; history; text; internal format)
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 * A254404 A254403 A075688

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

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Last modified January 20 04:14 EST 2019. Contains 319323 sequences. (Running on oeis4.)