A328482 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).

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, 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, 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

Offset: 0

Author

Antti Karttunen, Oct 19 2019

Keywords

• nonn

Examples

			Terms of A129912 (numbers that are products of distinct primorial numbers) begin as: 1, 2, 6, 12, 30, 60, 180, 210, 360, 420, 1260, ...
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).
Number 21 is expressed as 21 = 12 + 6 + 2 + 1, thus a(21) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..30030
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A129912, A328481, A328483.

Cf. also A267263.

Programs

PARI

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 || tA129912
prepare_A129912_upto(n) = { my(xs=List([]), k=0); while(kA129912(k), listput(xs,k))); List(Vecrev(xs)); };
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); };
A328482(n) = number_of_distinct_terms_in_greedy_sum(n,prepare_A129912_upto(n));

Formula

a(A129912(n)) = a(A002110(n)) = 1.

For all n, a(n) <= A328481(n).