A256623 Number of distinct n-digit patterns in base 10 such that the pattern and its reverse are prime.

4, 5, 29, 102, 796, 4769, 35905, 267789, 2101184, 16809690, 137487157, 1147385627, 9745119882

Offset: 1

Author

Russell Y. Webb, Jul 11 2015

Keywords

• nonn
• base
• more

Comments

Here, distinct numbers means under reversal. 13 and 31 are the same pattern under reversal and only count as one. The sequence can be calculated from the number of palindrome primes (A016115), p_i, and number of reversal primes (A048054), r_i. X_i = (r_i - p_i)/2 + p_i. The (r_i - p_i) term is always even, by construction (it is the count of reversible primes that are not their own reverse).

This sequence is the set cardinality of the prime numbers under a base-10 digit reversal identity operator.

Since there are no palindrome primes with even digits > 11 we know that the even entries are the same as half the number of reversible primes.

Crossrefs

Cf. A016115, A048054.

Formula

a(n) = (A048054(n) + A016115(n))/2.

Extensions

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