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Semiprimes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9), without digits "0".
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%I #14 Mar 31 2022 12:34:46

%S 15,21,26,34,38,39,51,58,62,65,74,82,85,87,93,95,115,121,122,123,129,

%T 133,134,142,143,145,155,158,159,177,178,183,185,187,213,214,215,217,

%U 218,219,221,226,247,249,254,259,262,265,267,274,278

%N Semiprimes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9), without digits "0".

%C This is to semiprimes A001358 as A220488 is to primes A000040.

%H Harvey P. Dale, <a href="/A211375/b211375.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 15 because 15 = 3*5 is semiprime, "1" is a nonprime digit, and "5" is a prime digit.

%t SemiprimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; fQ[n_] := Module[{d = IntegerDigits[n]}, SemiprimeQ[n] && Intersection[d, {2, 3, 5, 7}] != {} && Intersection[d, {1, 4, 6, 8, 9}] != {} && ! MemberQ[d, 0]]; Select[Range[278], fQ] (* _T. D. Noe_, Feb 09 2013 *)

%t spQ[n_]:=PrimeOmega[n]==2&&FreeQ[IntegerDigits[n],0]&&Count[ IntegerDigits[ n],_?PrimeQ]>0&&Count[IntegerDigits[n],_?(!PrimeQ[#]&)]>0; Select[ Range[ 300],spQ] (* _Harvey P. Dale_, Mar 31 2022 *)

%Y Cf. A001358, A220488.

%K nonn,base,easy,less

%O 1,1

%A _Jonathan Vos Post_, Feb 06 2013