A324383 a(n) is the minimal number of primorials that add to A322827(n).

1, 1, 1, 2, 2, 1, 2, 2, 2, 6, 1, 6, 4, 2, 4, 4, 8, 6, 6, 10, 8, 1, 10, 22, 4, 6, 2, 12, 8, 4, 4, 2, 8, 16, 6, 4, 24, 6, 8, 14, 26, 18, 1, 26, 20, 6, 18, 30, 6, 12, 2, 14, 16, 2, 10, 16, 8, 6, 4, 8, 6, 2, 4, 4, 12, 14, 14, 18, 18, 12, 16, 32, 42, 28, 6, 22, 32, 24, 24, 42, 46, 32, 18, 20, 30, 1, 24, 54, 38, 26, 14, 44, 34, 8

Offset

0,4

Comments

a(n) is odd if and only if n is one of the terms of A000975: 1, 2, 5, 10, 21, 42, 85, ..., in which case A322827(n) will be one of primorials (A002110), and a(n) = 1. This happens because A276150 is even for all multiples of four, and a product of two or more primorials > 1 is always a multiple of 4. Note that the same property does not hold in factorial system: 36 = 3!*3!, but A034968(36) = 3 as 36 = 4!+3!+3!.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10922

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Index entries for sequences related to binary expansion of n

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Formula

a(n) = A276150(A322827(n)).

a(n) = A324386(A003188(n)).

Prog

(PARI)
A276150(n) = { my(s=0, m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A322827(n) = if(!n, 1, my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2, #bits, if(bits[i]==bits[i-1], rl++, listput(o, rl))); listput(o, rl); my(es=Vecrev(Vec(o)), m=1); for(i=1, #es, m *= prime(i)^es[i]); (m));
A324383(n) = A276150(A322827(n));

Crossrefs

Cf. A000975 (positions of ones), A002110, A003188, A025487, A276150, A322827, A324342, A324382.

Cf. also A324386, A324387 (permutations of this sequence).

Sequence in context: A029286 A286221 A321347 * A342789 A050333 A343189

Adjacent sequences: A324380 A324381 A324382 * A324384 A324385 A324386

Keyword

nonn

Author

Antti Karttunen, Feb 27 2019

Status

approved