A173956 n-th primorial modulo n.

0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, 10, 0, 12, 0, 10, 0, 0, 0, 6, 20, 0, 3, 14, 0, 0, 0, 22, 0, 0, 0, 6, 0, 0, 0, 30, 0, 0, 0, 22, 30, 0, 0, 18, 21, 40, 0, 26, 0, 30, 0, 42, 0, 0, 0, 30, 0, 0, 42, 18, 0, 0, 0, 34, 0, 0, 0, 30, 0, 0, 60, 38, 0, 0, 0, 50, 12, 0, 0, 42, 0, 0, 0, 66, 0, 30, 0

Offset

1,4

Comments

Very similar to A076998.

For all n, a(A013929(n)) != 0, and a(A005117(n)) = 0. - Michel Marcus, Sep 03 2013 and Antti Karttunen, Nov 20 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A002110(n) mod n. - Michel Marcus, Sep 03 2013

Example

a(9) = p(9)# mod 9 = 23# mod 9 = 2*3*5*7*11*13*17*19*23 mod 9 = 6.

Mathematica

Array[Mod[Product[Prime@ i, {i, #}], #] &, 91] (* Michael De Vlieger, Nov 20 2017 *)
Module[{nn=100, prlm}, prlm=FoldList[Times, Prime[Range[nn]]]; Mod[ #[[1]], #[[2]]]&/@ Thread[{prlm, Range[nn]}]] (* Harvey P. Dale, May 14 2022 *)

Prog

(PARI) a(n) =  prod(i=1, n, prime(i)) % n; \\ Michel Marcus, Sep 03 2013

Crossrefs

Cf. A002110, A005117 (the positions of zeros).

Differs from A076998 for the first time at n=16, where a(16) = 10, while A076998(16) = 2.

Sequence in context: A059286 A345940 A076998 * A306078 A284273 A083927

Adjacent sequences: A173953 A173954 A173955 * A173957 A173958 A173959

Keyword

easy,nonn

Author

Carl R. White, Mar 03 2010

Status

approved