A358003 Least composite number k such that there are n digits in the intersection of the sets of digits of k and of the juxtaposition of prime factors of k (apart from multiplicity).

4, 12, 95, 132, 1972, 12305, 104392, 1026934, 10298746, 102367895, 1023485967

Offset: 0

Author

Jean-Marc Rebert, Oct 24 2022

Keywords

• nonn
• base
• fini
• full

Examples

			a(0) = 4 = (2*2) there are 0 digits in the intersection of {4} and {2}, and no lesser composite with this property exists.
a(1) = 12 = (2*2 * 3)
a(2) = 95 = (5 * 19)
a(3) = 132 = (2*2 * 3 * 11)
a(4) = 1972 = (2*2 * 17 * 29)
a(5) = 12305 = (5 * 23 * 107)
a(6) = 104392 = (2*2*2 * 13049)
a(7) = 1026934 = (2 * 463 * 1109)
a(8) = 10298746 = (2 * 1069 * 4817)
a(9) = 102367895 = (5 * 7 * 109 * 26833)
a(10) = 1023485967 = (3*3 * 7 * 16245809)
		

Programs

PARI

card(k)=my(u=Set(digits(k)), m=factor(k), v=[]); for(i=1, #m~, v=setunion(v, Set(digits(m[i, 1])))); #setintersect(u, v)
a(n)=if(n>10,return(0));forcomposite(k=10^(n-1), ,x=card(k);if(x==n,return(k)))