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A278159 Run length transform of primorials, A002110. 4
1, 2, 2, 6, 2, 4, 6, 30, 2, 4, 4, 12, 6, 12, 30, 210, 2, 4, 4, 12, 4, 8, 12, 60, 6, 12, 12, 36, 30, 60, 210, 2310, 2, 4, 4, 12, 4, 8, 12, 60, 4, 8, 8, 24, 12, 24, 60, 420, 6, 12, 12, 36, 12, 24, 36, 180, 30, 60, 60, 180, 210, 420, 2310, 30030, 2, 4, 4, 12, 4, 8, 12, 60, 4, 8, 8, 24, 12, 24, 60, 420, 4, 8, 8, 24, 8, 16, 24, 120, 12, 24, 24, 72, 60, 120, 420 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Like every run length transform this sequence satisfies for all i, j: A278222(i) = A278222(j) => a(i) = a(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences computed with run length transform

FORMULA

a(n) = A124859(A005940(1+n)).

EXAMPLE

For n=7, "111" in binary, there is a run of 1-bits of length 3, thus a(7) = product of A002110(3), = A002110(3) = 30.

For n=39, "10111" in binary, there are two runs, of lengths 1 and 3, thus a(39) = A002110(1) * A002110(3) = 2*30 = 60.

MATHEMATICA

f[n_] := Product[Prime[k], {k, 1, n}]; Table[Times @@ (f[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 94}] (* Jean-Fran├žois Alcover, Jul 11 2017 *)

PROG

(Scheme)

(define (A278159 n) (fold-left (lambda (a r) (* a (A002110 r))) 1 (bisect (reverse (binexp->runcount1list n)) (- 1 (modulo n 2)))))

;; See A227349 for the required other functions.

CROSSREFS

Cf. A002110, A005940, A124859, A227349, A246660, A278161, A278222.

Sequence in context: A138949 A138951 A163370 * A071796 A121699 A080404

Adjacent sequences:  A278156 A278157 A278158 * A278160 A278161 A278162

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Nov 16 2016

STATUS

approved

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Last modified June 21 16:29 EDT 2021. Contains 345365 sequences. (Running on oeis4.)