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

1,1

Comments

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

Links

Table of n, a(n) for n=1..18.

Example

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.

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));

Crossrefs

Sequence in context: A087112 A077554 A390526 * A262812 A287296 A275197

Adjacent sequences: A382898 A382899 A382900 * A382902 A382903 A382904

Keyword

nonn,base,fini,full

Author

Zak Seidov and Robert Israel, Apr 08 2025

Status

approved