A377876 The n-th primorial number reduced modulo 27.

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, 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, 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

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..19683

Index entries for sequences related to primorial numbers

Formula

a(n) = A002110(n) mod 27.

Maple

R:= 1: p:= 1: v:= 1:
for i from 1 to 100 do
  p:= nextprime(p); v:= p*v mod 27;
  R:= R, v;
od:
R; # Robert Israel, Nov 12 2024

Mathematica

Mod[FoldList[Times, 1, Prime[Range[87]]], 27] (* James C. McMahon, Nov 12 2024 *)

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A377876(n) = (A002110(n)%27);
(PARI)
up_to = 105;
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); };
v377876 = A377876list(up_to);
A377876(n) = v377876[1+n];
(Python)
from functools import reduce
from sympy import primerange, prime
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

Crossrefs

Cf. A002110, A377872.

Cf. also A086360, A377877.

Sequence in context: A050125 A178667 A281881 * A206493 A359256 A304085

Adjacent sequences: A377873 A377874 A377875 * A377877 A377878 A377879

Keyword

nonn

Author

Antti Karttunen, Nov 12 2024

Status

approved