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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.

%I A348187 #23 Oct 06 2024 11:32:52
%S A348187 12,22,31,122,132,312,322,2323,3312,14421,23222,24243,33333,51243,
%T A348187 333424,342332,432241,523233,1333232,1432243,2424341,2442253,5134334,
%U A348187 15232343,24243232,24424243,25514234,26134354,32334533,33252335,33341415,33343412,34332425,43523432,53224343
%N 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.
%e A348187 12 is a term because omega([11, 12]) gives [1, 2], the digits of 12.
%e A348187 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].
%o A348187 (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);}
%o A348187 lista(nn) = {my(list = List()); for (n=1, nn, my(w=vecn(n)); for (k=1, #w, listput(list, w[k]));); Set(list);}
%Y A348187 Cf. A001221 (omega), A323083 (following), A348266 (preceding).
%K A348187 nonn,base
%O A348187 1,1
%A A348187 _Michel Marcus_, Oct 12 2021