A328482 - OEIS

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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

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OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..30030

Index entries for sequences related to primorial numbers

FORMULA

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

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

EXAMPLE

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.

PROG

(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 || t<o-1, return(0)); if(t==0, return(n==1)); o=t); }; \\ From A129912

prepare_A129912_upto(n) = { my(xs=List([]), k=0); while(k<n, k++; if(isA129912(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));

CROSSREFS

Cf. A002110, A129912, A328481, A328483.

Cf. also A267263.

Sequence in context: A224702 A267263 A060130 * A371091 A257695 A257694

Adjacent sequences: A328479 A328480 A328481 * A328483 A328484 A328485

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2019

STATUS

approved