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A115366
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a(n) = the number of values of k <= 10^n such that sqrt(k*(k+1)*(k+2)*(k+3)+1) is prime.
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1
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1, 9, 50, 313, 2188, 17075, 139484, 1179766, 10220078, 90159466, 806928985, 7302511765
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OFFSET
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0,2
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COMMENTS
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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...
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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