A216150 Smallest prime q such that sum(i=1..n-1, q mod(prime(i))) == q mod prime(n).

7, 2, 11, 71, 331, 13, 4217, 4643, 16381, 6007, 225217, 260339, 4772483, 117351431, 130554581, 2499413753

Offset

2,1

Comments

The sequence is infinite.

Links

Table of n, a(n) for n=2..17.

Example

n = 2: p_n = 3, q = 7,7 (mod 2) = 1 and  1 = 7 (mod 3);
n = 3: p_n = 5, q = 2, 2 (mod(2,3)) = (0,2) and  0 + 2 = 2 = 2 (mod 5);
n = 4: p_n = 7, q = 11, 11 (mod(2,3,5)) = (1,2,1) and  1 + 2 + 1 = 4 = 11 (mod 7);
n = 5: p_n = 11, q = 71, 71 (mod(2,3,5,7)) = (1,2,1,1) and  1 + 2 + 1 + 1 = 5 = 71 (mod 11).

Prog

(PARI) for(n=2, 50, p=prime(n); q=2; while(sum(i=1, n-1, q%prime(i))<>q%p, q=nextprime(q+1)); print(n", "q))

Crossrefs

Sequence in context: A248283 A147677 A090243 * A145338 A104586 A323995

Adjacent sequences: A216147 A216148 A216149 * A216151 A216152 A216153

Keyword

nonn,more,hard

Author

Zak Seidov, Sep 02 2012

Status

approved