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Search: id:A115366
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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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+0
1
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| 1, 9, 50, 313, 2188, 17075, 139484, 1179766, 10220078, 90159466
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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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MATHEMATICA
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fQ[x_] := PrimeQ(AT) Round(AT) Sqrt[x(x + 1)(x + 2)(x + 3) + 1]; c = k = 0; Do[ While[k <= 10^n, If[ fQ(AT)k, c++ ]; k++ ]; Print(AT)c, {n, 0, 9}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 17 2006).
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}] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 01 2006)
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PROGRAM
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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", ") ) }
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CROSSREFS
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Cf. A006880.
Adjacent sequences: A115363 A115364 A115365 this_sequence A115367 A115368 A115369
Sequence in context: A084367 A006974 A007681 this_sequence A002462 A034814 A034816
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Mar 07 2006
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Apr 24 2006
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