A059955 a(n) = floor( prime(n)!/lcm(1..prime(n)) ) modulo prime(n).

1, 2, 5, 10, 3, 10, 4, 3, 28, 17, 18, 30, 20, 41, 42, 14, 19, 30, 37, 63, 50, 7, 12, 83, 30, 91, 19, 69, 91, 97, 56, 22, 80, 39, 137, 44, 9, 154, 19, 37, 141, 141, 168, 126, 183, 200, 205, 136, 55, 95, 204, 126, 213, 230, 68, 63, 158, 202, 162, 102, 182, 104, 38, 165

Offset

2,2

Comments

a(n) gives also the smallest coefficient for which the multiple M of lcm(1 through p(n)-1) satisfies p(n) divides M + 1. This computes the solution of the puzzle requiring the smallest number such that grouping in 2's, 3's, etc. up to the n-th prime,all leave a remainder of one except the last which leaves no remainder.

Links

Table of n, a(n) for n=2..65.

Example

a(2)=1 because prime(2)=3 and floor(3!/lcm(1,2,3)) mod 3 = 1 mod 3 = 1;
a(3)=2 because prime(3)=5 and floor(5!/lcm(1,2,3,4,5)) mod 5 = 2 mod 5 = 2;
a(4)=5 because prime(4)=7 and floor(7!/lcm(1,2,3,4,5,6,7)) mod 7 = 12 mod 7 = 5;
a(7)=10 because prime(7)=17 and floor(17!/lcm(1,2,...,17)) mod 17 = 29030400 mod 17 = 10.

Maple

for n from 2 to 150 do printf(`%d, `, floor(ithprime(n)!/ilcm(i $ i=1..ithprime(n))) mod ithprime(n) ); od:

Prog

(Magma) [Floor( Factorial(p)/Lcm([1..p]) ) mod p: p in PrimesInInterval(3, 400)]; // Bruno Berselli, Feb 08 2015

Crossrefs

Cf. A003418, A025527, A099796.

Sequence in context: A306679 A125974 A218336 * A099796 A022831 A064365

Adjacent sequences: A059952 A059953 A059954 * A059956 A059957 A059958

Keyword

nonn

Author

Lekraj Beedassy, Mar 13 2001

Extensions

More terms from James A. Sellers, Mar 15 2001

Status

approved