A382901 Semiprimes that can be expressed using at most one of each of the semiprime digits 4, 6, 9 using concatenation and the arithmetic operations +, -, *, /, ^.

4, 6, 9, 10, 15, 33, 46, 49, 55, 58, 65, 69, 94, 469, 649, 694, 4087, 4105

Offset: 1

Author

Zak Seidov and Robert Israel, Apr 08 2025

Keywords

• nonn
• base
• fini
• full

Comments

Concatenation is not allowed with expressions, only digits, e.g. (9-6)4 = 34 is not allowed.

Examples

			46, 49, 69, 94, 469, 649 and 694 are concatenations.
10 = 4 + 6.
15 = 6 + 9.
33 = 4 * 6 + 9.
55 = 46 + 9.
58 = 6 * 9 + 4.
65 = 69 - 4.
4087 = 4^6 - 9.
4105 = 4^6 + 9.
		

Programs

Maple

A2:= select(t -> numtheory:-bigomega(t)=2, map(t -> (t[1]+t[2],10*t[1]+t[2]),convert(combinat:-permute([4,6,9],2),set))):
A3:= select(t -> t::integer and numtheory:-bigomega(t) = 2, map(t -> (t[1]+t[2]+t[3],t[1]+t[2]-t[3],t[1]*t[2]+t[3],t[1]*t[2]-t[3],100*t[1]+10*t[2]+t[3],10*t[1]+t[2]-t[3],10*t[1]+t[2]+t[3],t[1]^t[2]+t[3],t[1]^t[2]-t[3],
(10*t[1]+t[2])/t[3]), convert(combinat:-permute([4,6,9]),set))):
sort(convert({4,6,9,op(A2),op(A3)},list));