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%I #10 Oct 19 2019 21:26:23
%S 0,1,1,2,1,2,1,2,2,3,2,3,1,2,2,3,2,3,2,3,3,4,3,4,1,2,2,3,2,3,1,2,2,3,
%T 2,3,2,3,3,4,3,4,2,3,3,4,3,4,3,4,4,5,4,5,2,3,3,4,3,4,1,2,2,3,2,3,2,3,
%U 3,4,3,4,2,3,3,4,3,4,3,4,4,5,4,5,2,3,3,4,3,4,2,3,3,4,3,4,3,4,4,5,4,5,3,4,4,5
%N Number of distinct terms required when n is expressed as a greedy sum of terms of A129912 (number of nonzero digits when n is expressed in greedy A129912-base).
%H Antti Karttunen, <a href="/A328482/b328482.txt">Table of n, a(n) for n = 0..30030</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(A129912(n)) = a(A002110(n)) = 1.
%F For all n, a(n) <= A328481(n).
%e Terms of A129912 (numbers that are products of distinct primorial numbers) begin as: 1, 2, 6, 12, 30, 60, 180, 210, 360, 420, 1260, ...
%e Number 5 is expressed as 5 = 2 + 2 + 1 = 2*2 + 1*1, when always choosing the largest term which is <= {what is remaining of the original number}. Thus a(5) = 2 (number of distinct terms used, 1 and 2).
%e Number 21 is expressed as 21 = 12 + 6 + 2 + 1, thus a(21) = 4.
%o (PARI)
%o isA129912(n) = { my(o=valuation(n, 2), t); if(o<1||n<2, return(n==1)); n>>=o; forprime(p=3, , t=valuation(n, p); n/=p^t; if(t>o || t<o-1, return(0)); if(t==0, return(n==1)); o=t); }; \\ From A129912
%o prepare_A129912_upto(n) = { my(xs=List([]), k=0); while(k<n, k++; if(isA129912(k), listput(xs,k))); List(Vecrev(xs)); };
%o number_of_distinct_terms_in_greedy_sum(n,terms) = { my(c=0); while(n,if(terms[1] > n, listpop(terms,1), c++; n %= terms[1])); (c); };
%o A328482(n) = number_of_distinct_terms_in_greedy_sum(n,prepare_A129912_upto(n));
%Y Cf. A002110, A129912, A328481, A328483.
%Y Cf. also A267263.
%K nonn
%O 0,4
%A _Antti Karttunen_, Oct 19 2019
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