A348187 Integers m with k digits (for some k) that lie in an interval of k integers and the digits of m are the total number of distinct prime factors of all the integers in that interval.

12, 22, 31, 122, 132, 312, 322, 2323, 3312, 14421, 23222, 24243, 33333, 51243, 333424, 342332, 432241, 523233, 1333232, 1432243, 2424341, 2442253, 5134334, 15232343, 24243232, 24424243, 25514234, 26134354, 32334533, 33252335, 33341415, 33343412, 34332425, 43523432, 53224343

Offset: 1

Author

Michel Marcus, Oct 12 2021

Keywords

• nonn
• base

Examples

			12 is a term because omega([11, 12]) gives [1, 2], the digits of 12.
33333 is a term because omega([33332, 33333, 33334, 33335, 33336]) but also omega([33333, 33334, 33335, 33336, 33337]) both give [3, 3, 3, 3, 3].
		

Crossrefs

Cf. A001221 (omega), A323083 (following), A348266 (preceding).

Programs

PARI

vecn(n) = {my(list = List()); for (k=10^(n-1), 10^n-1-n, my(w = apply(omega, vector(n, i, k+i-1))); my(m = fromdigits(w)); if ((m>=k) && (m<=k+n-1), listput(list, m));); Set(list);}
lista(nn) = {my(list = List()); for (n=1, nn, my(w=vecn(n)); for (k=1, #w, listput(list, w[k]));); Set(list);}