A084700 Smallest k such that k*prime(i)+1 is prime for i = 1 to n.

1, 2, 2, 6, 6, 6, 6, 192660, 437286240, 37202202450, 148684126500, 2258581791060, 161082438032880

Offset

1,2

Comments

For n > 7, a(n) == 0 mod 30.

Conjecture: log a(n) ~ C n log n. - Thomas Ordowski, Nov 20 2017

Links

Table of n, a(n) for n=1..13.

Example

a(4) = a(5) = a(6) = a(7) = 6 as 2*6+1 = 13, 3*6+1 = 19, 5*6+1 = 31, 7*6+1 = 43, 11*6+1 = 67, 13*6+1 = 79, 17*6+1 = 103 are all primes.

Mathematica

k = 2; Do[ While[ Union[ PrimeQ[ Table[ k*Prime[i] + 1, {i, 1, n}]]] != {True}, k+=2]; Print[k], {n, 2, 8}]

Crossrefs

Cf. A084701.

Sequence in context: A259225 A300951 A077081 * A122766 A291185 A320140

Adjacent sequences: A084697 A084698 A084699 * A084701 A084702 A084703

Keyword

more,nonn

Author

Amarnath Murthy, Jun 08 2003

Extensions

Edited and extended by Robert G. Wilson v and Don Reble, Jun 15 2003

Terms 11, 12 and 13 found by Phil Carmody using his GenSv generic siever, Mar 08 2004

Status

approved