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

%I A264815 #24 Apr 27 2025 10:35:19
%S A264815 4,6,9,10,14,15,21,22,25,26,33,34,35,39,49,51,55,62,65,74,77,85,91,93,
%T A264815 111,119,121,142,143,146,155,158,169,185,187,194,202,213,214,217,219,
%U A264815 221,226,237,259,262,289,291,298,302,303,314,321,334,339,341,355
%N A264815 Semirps: a semirp (or semi-r-p) is a semiprime r*p with r and p both reversed primes.
%C A264815 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).
%C A264815 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.
%H A264815 Danny Rorabaugh, <a href="/A264815/b264815.txt">Table of n, a(n) for n = 1..10000</a>
%F A264815 [A007500]^2, sorted.
%e A264815 9 is in the list because 9 = 3*3 is a semiprime and reverse(3) = 3 is prime.
%e A264815 143 is in the list because 143 = 11*13 is a semiprime and both reverse(11) = 11 and reverse(13) = 31 are prime.
%t A264815 With[{nn=250},Take[Union[Times@@@Select[Tuples[IntegerReverse/@Prime[Range[nn]],2],AllTrue[#,PrimeQ]&]],60]] (* _Harvey P. Dale_, Apr 27 2025 *)
%o A264815 (Sage)
%o A264815 reverse = lambda n: sum([10^i*int(str(n)[i]) for i in range(len(str(n)))])
%o A264815 def is_semirp(n):
%o A264815   F = factor(n)
%o A264815   if sum([f[1] for f in F])==2:
%o A264815     r, p = F[0][0], F[-1][0]
%o A264815     if is_prime(reverse(r)) and is_prime(reverse(p)): return True
%o A264815 [a for a in range(1,356) if is_semirp(a)] # _Danny Rorabaugh_, Nov 25 2015
%Y A264815 Cf. A001358, A006567, A007500, A097393, A109019, A115670.
%K A264815 nonn,base
%O A264815 1,1
%A A264815 _Danny Rorabaugh_, Nov 25 2015