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A278159 Run length transform of primorials, A002110.

%I A278159 #22 Feb 04 2022 11:19:10
%S A278159 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,
%T A278159 30,60,210,2310,2,4,4,12,4,8,12,60,4,8,8,24,12,24,60,420,6,12,12,36,
%U A278159 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
%N A278159 Run length transform of primorials, A002110.
%C A278159 Like every run length transform this sequence satisfies for all i, j: A278222(i) = A278222(j) => a(i) = a(j).
%H A278159 Antti Karttunen, <a href="/A278159/b278159.txt">Table of n, a(n) for n = 0..8192</a>
%H A278159 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A278159 <a href="/index/Ru#rlt">Index entries for sequences computed with run length transform</a>
%F A278159 a(n) = A124859(A005940(1+n)).
%e A278159 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.
%e A278159 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.
%t A278159 f[n_] := Product[Prime[k], {k, 1, n}]; Table[Times @@ (f[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 94}] (* _Jean-François Alcover_, Jul 11 2017 *)
%o A278159 (Scheme)
%o A278159 (define (A278159 n) (fold-left (lambda (a r) (* a (A002110 r))) 1 (bisect (reverse (binexp->runcount1list n)) (- 1 (modulo n 2)))))
%o A278159 ;; See A227349 for the required other functions.
%o A278159 (Python)
%o A278159 from math import prod
%o A278159 from re import split
%o A278159 from sympy import primorial
%o A278159 def RLT(n,f):
%o A278159     """ run length transform of a function f """
%o A278159     return prod(f(len(d)) for d in split('0+', bin(n)[2:]) if d != '') if n > 0 else 1
%o A278159 def A278159(n): return RLT(n,primorial) # _Chai Wah Wu_, Feb 04 2022
%Y A278159 Cf. A002110, A005940, A124859, A227349, A246660, A278161, A278222.
%K A278159 nonn,base
%O A278159 0,2
%A A278159 _Antti Karttunen_, Nov 16 2016