A264815 Semirps: a semirp (or semi-r-p) is a semiprime r*p with r and p both reversed primes.

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 39, 49, 51, 55, 62, 65, 74, 77, 85, 91, 93, 111, 119, 121, 142, 143, 146, 155, 158, 169, 185, 187, 194, 202, 213, 214, 217, 219, 221, 226, 237, 259, 262, 289, 291, 298, 302, 303, 314, 321, 334, 339, 341, 355

Offset: 1

Author

Danny Rorabaugh, Nov 25 2015

Keywords

• nonn
• base

Comments

A semiprime (A001358) is the product of two prime, not necessarily distinct. A semiprime is in this list if those two primes (A000040) are reversed primes (A004087).

Since A007500 is the intersection of A000040 and A004087, this sequence is also the sorted list of all r*p with r and p in A007500.

Examples

			9 is in the list because 9 = 3*3 is a semiprime and reverse(3) = 3 is prime.
143 is in the list because 143 = 11*13 is a semiprime and both reverse(11) = 11 and reverse(13) = 31 are prime.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A006567, A007500, A097393, A109019, A115670.

Programs

Mathematica

With[{nn=250},Take[Union[Times@@@Select[Tuples[IntegerReverse/@Prime[Range[nn]],2],AllTrue[#,PrimeQ]&]],60]] (* Harvey P. Dale, Apr 27 2025 *)

Sage

reverse = lambda n: sum([10^i*int(str(n)[i]) for i in range(len(str(n)))])
def is_semirp(n):
  F = factor(n)
  if sum([f[1] for f in F])==2:
    r, p = F[0][0], F[-1][0]
    if is_prime(reverse(r)) and is_prime(reverse(p)): return True
[a for a in range(1,356) if is_semirp(a)] # Danny Rorabaugh, Nov 25 2015

Formula

[A007500]^2, sorted.