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

1,1

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.

Links

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

Formula

[A007500]^2, sorted.

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A129336 A226526 A103607 * A351096 A108574 A157931

Adjacent sequences: A264812 A264813 A264814 * A264816 A264817 A264818

Keyword

nonn,base

Author

Danny Rorabaugh, Nov 25 2015

Status

approved