A328483 Maximum number of times any term appears when n is expressed as a greedy sum of terms of A129912 (maximal digit when n is expressed in greedy A129912-base).

0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1

Offset

0,5

Comments

Apparently no term is larger than 2.

In the initial prefix of 30031 terms, the longest run of 1's is 4 and 2's occur only in runs of lengths 2, 8, 38, 68, 218 and 428. - Bill McEachen, Nov 21 2019, clarified by Antti Karttunen, Nov 23 2019

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.

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 when always choosing the largest term which is <= {what is remaining of the original number}. Thus a(5) = 2 as the most frequent term (2) occurs twice.
Number 21 is expressed as 21 = 12 + 6 + 2 + 1, thus a(21) = 1 as no term occurs more than once.
Number 720 is expressed as 720 = 420 + 210 + 60 + 30, thus a(720) = 1 as no term occurs twice. Note that 720 = 2*360, so an algorithm which would search for an optimal result would yield a different value at n=720.

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)); };
max_factor_of_terms_in_greedy_sum(n, terms) = { my(m=0); while(n, if(terms[1] > n, listpop(terms, 1), m = max(m, (n\terms[1])); n %= terms[1])); (m); };
A328483(n) = max_factor_of_terms_in_greedy_sum(n, prepare_A129912_upto(n));

Crossrefs

Cf. A002110, A129912, A328481, A328482.

Sequence in context: A128016 A128017 A096285 * A321856 A175078 A121561

Adjacent sequences: A328480 A328481 A328482 * A328484 A328485 A328486

Keyword

nonn

Author

Antti Karttunen, Oct 19 2019

Status

approved