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A377876 The n-th primorial number reduced modulo 27.

%I A377876 #15 Nov 13 2024 17:16:35
%S A377876 1,2,6,3,21,15,6,21,21,24,21,3,3,15,24,21,6,3,21,3,24,24,6,12,15,24,
%T A377876 21,3,24,24,12,12,6,12,21,24,6,24,24,12,24,3,3,6,24,3,3,12,3,6,24,3,
%U A377876 15,24,3,15,3,24,24,6,12,21,24,24,12,3,6,15,6,3,21,15,12,3,12,12,6,12,12,6,24,12,3,24,24,6,12,15
%N A377876 The n-th primorial number reduced modulo 27.
%H A377876 Antti Karttunen, <a href="/A377876/b377876.txt">Table of n, a(n) for n = 0..19683</a>
%H A377876 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A377876 a(n) = A002110(n) mod 27.
%p A377876 R:= 1: p:= 1: v:= 1:
%p A377876 for i from 1 to 100 do
%p A377876   p:= nextprime(p); v:= p*v mod 27;
%p A377876   R:= R,v;
%p A377876 od:
%p A377876 R; # _Robert Israel_, Nov 12 2024
%t A377876 Mod[FoldList[Times,1,Prime[Range[87]]],27] (* _James C. McMahon_, Nov 12 2024 *)
%o A377876 (PARI)
%o A377876 A002110(n) = prod(i=1,n,prime(i));
%o A377876 A377876(n) = (A002110(n)%27);
%o A377876 (PARI)
%o A377876 up_to = 105;
%o A377876 A377876list(up_to_n) = { my(m=27, v=vector(1+up_to_n), pr=1); v[1] = 1; for(n=1, up_to_n, pr *= Mod(prime(n),m); v[1+n] = lift(pr)); (v); };
%o A377876 v377876 = A377876list(up_to);
%o A377876 A377876(n) = v377876[1+n];
%o A377876 (Python)
%o A377876 from functools import reduce
%o A377876 from sympy import primerange, prime
%o A377876 def A377876(n): return reduce(lambda x,y:x*y%27,primerange(prime(n)+1)) if n else 1 # _Chai Wah Wu_, Nov 12 2024
%Y A377876 Cf. A002110, A377872.
%Y A377876 Cf. also A086360, A377877.
%K A377876 nonn
%O A377876 0,2
%A A377876 _Antti Karttunen_, Nov 12 2024