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URL: https://oeis.org/A115366

⇱ A115366 - OEIS

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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
1, 9, 50, 313, 2188, 17075, 139484, 1179766, 10220078, 90159466, 806928985, 7302511765
OFFSET
0,2
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...
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", ") ) }
(Python)
from sympy import isprime
def A115366(n): return sum(1 for k in range(1, 10**n+1) if isprime(k*(k+3)+1)) # Chai Wah Wu, Jun 19 2024
CROSSREFS
Cf. A006880.
Sequence in context: A231413 A007681 A279972 * A188210 A308646 A338510
KEYWORD
nonn,more
AUTHOR
Cino Hilliard, Mar 07 2006
EXTENSIONS
Edited by Don Reble, Apr 24 2006
a(10) from Michael S. Branicky, Jun 20 2024
a(11) from Michael S. Branicky, Jun 23 2024
STATUS
approved