A375784 Array read by rows: T(n,k) is the first number with n prime factors (counted with multiplicity) and n occurrences of decimal digit k.
101, 13, 2, 3, 41, 5, 61, 7, 83, 19, 1003, 115, 22, 33, 445, 55, 166, 77, 818, 299, 10002, 1113, 222, 333, 4244, 555, 2666, 777, 8828, 3999, 100002, 11011, 22122, 33332, 4444, 15555, 6666, 75777, 38888, 9999, 1000004, 1011112, 222220, 333330, 444244, 552555, 666366, 777770, 88888, 999996
Offset: 1
Examples
T(5,1) = 1011112 = 2^3 * 211 * 599 has 5 prime factors (counted with multiplicity) and 5 1's, and is the first such number.
Array starts
101 13 2 3 41 5 61 7 83 19
1003 115 22 33 445 55 166 77 818 299
10002 1113 222 333 4244 555 2666 777 8828 3999
100002 11011 22122 33332 4444 15555 6666 75777 38888 9999
1000004 1011112 222220 333330 444244 552555 666366 777770 88888 999996
Links
- Robert Israel, Table of n, a(n) for n = 1..150
Programs
-
Maple
F:= proc(v, x) local d, y, z, L, S, SS, Cands, t, i, k; for d from v do Cands:= NULL; if x = 0 then SS:= combinat:-choose([$1..d-1], v) else SS:= combinat:-choose([$1..d], v) fi; for S in SS do for y from 9^(d-v+1) to 9^(d-v+1)+9^(d-v)-1 do L:= convert(y, base, 9)[1..d-v+1]; L:= map(proc(s) if s < x then s else s+1 fi end proc, L); i:= 1; t:= 0: for k from 1 to d do if member(k, S) then t:= t + x*10^(k-1) else t:= t + L[i]*10^(k-1); i:= i+1; fi; od; Cands:= Cands, t od od; Cands:= sort([Cands]); for t in Cands do if numtheory:-bigomega(t)=v then return t fi od; od end proc: for i from 1 to 10 do seq(F(i, x), x=0..9) od; -
Mathematica
T[n_, k_]:=Module[{m=2}, While[PrimeOmega[m]!=n||Count[IntegerDigits[m], k]!=n, m++]; m]; Table[T[n, k], {n, 1, 5}, {k, 0, 9}]//Flatten (* Stefano Spezia, Aug 30 2024 *)