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A324383 a(n) is the minimal number of primorials that add to A322827(n). 5
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 (list; graph; refs; listen; history; text; internal format)
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 * A050333 A271775 A143999

Adjacent sequences:  A324380 A324381 A324382 * A324384 A324385 A324386

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 27 2019

STATUS

approved

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Last modified May 19 10:55 EDT 2019. Contains 323390 sequences. (Running on oeis4.)