A211375 Semiprimes that have both prime digits (2,3,5,7) and nonprime digits (1,4,6,8,9), without digits "0".

15, 21, 26, 34, 38, 39, 51, 58, 62, 65, 74, 82, 85, 87, 93, 95, 115, 121, 122, 123, 129, 133, 134, 142, 143, 145, 155, 158, 159, 177, 178, 183, 185, 187, 213, 214, 215, 217, 218, 219, 221, 226, 247, 249, 254, 259, 262, 265, 267, 274, 278

Offset: 1

Author

Jonathan Vos Post, Feb 06 2013

Keywords

• nonn
• base
• easy
• less

Comments

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

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A220488.

Programs

Mathematica

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 *)
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 *)