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

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

Offset

1,1

Comments

The count includes palindromes.

Links

Table of n, a(n) for n=1..15.

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A386231 A359922 A093149 * A284973 A239853 A209079

Adjacent sequences: A048051 A048052 A048053 * A048055 A048056 A048057

Keyword

base,nonn,more

Author

Jud McCranie

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

Status

approved