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

1,1

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.

Links

Table of n, a(n) for n=1..13.

Formula

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

Crossrefs

Cf. A016115, A048054.

Sequence in context: A042647 A266075 A041273 * A047169 A262034 A124482

Adjacent sequences: A256620 A256621 A256622 * A256624 A256625 A256626

Keyword

nonn,base,more

Author

Russell Y. Webb, Jul 11 2015

Extensions

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

Status

approved