A115366 a(n) = the number of values of k <= 10^n such that sqrt(k*(k+1)*(k+2)*(k+3)+1) is prime.

1, 9, 50, 313, 2188, 17075, 139484, 1179766, 10220078, 90159466

Offset

1,2

Comments

sqrt(k*(k+1)*(k+2)*(k+3)+1) = k^2 + 3*k + 1.

a(n)/A006880(n) ~= 1.78, 1.78, 1.7769, 1.7752, 1.7738, 1.7731. Conjecture: a(n)/A006880(n) -> 1.77...

Links

Table of n, a(n) for n=1..10.

Mathematica

c = 0; k = 1; Do[ While[k <= 10^n, If[ PrimeQ@ Round@ Sqrt[k(k + 1)(k + 2)(k + 3) + 1], c++ ]; k++ ]; Print@c, {n, 0, 9}] (* Robert G. Wilson v, May 01 2006 *)

Prog

(PARI) g(n)= { for(j=0, n, c=0; for(x=0, 10^j, y=round(sqrt(x*(x+1)*(x+2)*(x+3)+1)); if(ispseudoprime(y), c++)); print1(c", ") ) }

Crossrefs

Cf. A006880.

Sequence in context: A231413 A007681 A279972 * A188210 A308646 A338510

Adjacent sequences: A115363 A115364 A115365 * A115367 A115368 A115369

Keyword

nonn,more

Author

Cino Hilliard, Mar 07 2006

Extensions

Edited by Don Reble, Apr 24 2006

Status

approved