A048054 Number of n-digit reversible primes (emirps).

4, 9, 43, 204, 1499, 9538, 71142, 535578, 4197196, 33619380, 274932272, 2294771254, 19489886063, 167630912672, 1456476399463

Offset: 1

Author

Jud McCranie

Keywords

• base
• nonn
• more

Comments

The count includes palindromes.

Examples

			2, 3, 5 and 7 are 1-digit reversible primes, so a(1)=4.
		

Links

• J. L. Boal and J. H. Bevis, Permutable primes. Math. Mag., 55 (N0. 1, 1982), 38-41. [From _N. J. A. Sloane_, Jan 19 2012]
• Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Reversible primes, arXiv:2309.11380 [math.NT], 2023. See p. 36.

Crossrefs

Cf. A003684, A006567, A007628, A046732, A048051, A048052, A048053, A048895.

Programs

Mathematica

Count[Range[10^(# - 1), 10^# - 1], n_ /; And[PrimeQ@ n, PrimeQ@ FromDigits@ Reverse@ IntegerDigits@ n]] & /@ Range@ 7 (* Michael De Vlieger, Jul 14 2015 *)

Python

from sympy import isprime, primerange
def A048054(n):
    return len([p for p in primerange(10**(n-1),10**n)
                if isprime(int(str(p)[::-1]))]) # Chai Wah Wu, Aug 14 2014

Extensions

a(11)-a(13) from Giovanni Resta, Jul 19 2015

a(14)-a(15) from Cécile Dartyge, Bruno Martin, Joël Rivat, Igor E. Shparlinski, and Cathy Swaenepoel, Oct 05 2023