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Search: id:A098062
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| A098062 |
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Primes of the form n^2 + 4n + 8. |
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+0
3
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| 13, 29, 53, 173, 229, 293, 733, 1093, 1229, 1373, 2029, 2213, 3253, 4229, 4493, 5333, 7229, 7573, 9029, 9413, 10613, 13229, 13693, 15629, 18229, 18773, 21613, 24029, 26573, 27893, 31333, 33493, 37253, 41213, 42853, 46229, 47093, 54293, 55229
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Or, primes that are equal to the mean of 7 consecutive squares. - Zak Seidov (zakseidov(AT)gmail.com), Apr 14 2007
Sum of 7 consecutive squares starting with m^2 is equal to 7*(13 + 6*m + m^2) and mean is (13 + 6*m + m^2)=(m+3)^2+4. Hence a(n)=A005473(n+1). Note that only nonnegative m's are considered. - Zak Seidov (zakseidov(AT)gmail.com), Apr 14 2007
a(n)==1 (mod 4).
a(n)= A005473(n+1). - Zak Seidov, Apr 12 2007
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EXAMPLE
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13=(0^2+...+6^2)/7, 29=(2^2+...+8^2)/7=29, 53=(4^2+...+10^2)/7=53.
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MATHEMATICA
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Select[ Table[ n^2 + 4n + 8, {n, 240}], PrimeQ[ # ] &] (from Robert G. Wilson v Sep 14 2004)
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PROGRAM
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(PARI) for(n=0, 240, if(isprime(p=n^2+4*n+8), print1(p, ", "))) (Klaus Brockhaus)
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CROSSREFS
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Cf. A005473, A056899, A067201, A007591, A129389, A129412.
Sequence in context: A082285 A010337 A090866 this_sequence A094481 A045637 A065546
Adjacent sequences: A098059 A098060 A098061 this_sequence A098063 A098064 A098065
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KEYWORD
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nonn,new
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Sep 12 2004
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 14 2004
Edited by njas, Jul 02 2008 at the suggestion of R. J. Mathar
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