This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382901 #13 Apr 11 2025 07:58:31
%S A382901 4,6,9,10,15,33,46,49,55,58,65,69,94,469,649,694,4087,4105
%N 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 +, -, *, /, ^.
%C A382901 Concatenation is not allowed with expressions, only digits, e.g. (9-6)4 = 34 is not allowed.
%e A382901 46, 49, 69, 94, 469, 649 and 694 are concatenations.
%e A382901 10 = 4 + 6.
%e A382901 15 = 6 + 9.
%e A382901 33 = 4 * 6 + 9.
%e A382901 55 = 46 + 9.
%e A382901 58 = 6 * 9 + 4.
%e A382901 65 = 69 - 4.
%e A382901 4087 = 4^6 - 9.
%e A382901 4105 = 4^6 + 9.
%p A382901 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))):
%p A382901 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],
%p A382901 (10*t[1]+t[2])/t[3]), convert(combinat:-permute([4,6,9]),set))):
%p A382901 sort(convert({4,6,9,op(A2),op(A3)},list));
%K A382901 nonn,base,fini,full
%O A382901 1,1
%A A382901 _Zak Seidov_ and _Robert Israel_, Apr 08 2025