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A096788
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Numbers n such that both n and n+1 are composite numbers that add up to a prime of the form 4k+3).
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10
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9, 15, 21, 33, 35, 39, 51, 63, 65, 69, 75, 81, 95, 99, 105, 111, 119, 125, 135, 141, 153, 155, 165, 183, 189, 209, 215, 219, 221, 231, 243, 245, 249, 261, 273, 285, 299, 303, 309, 315, 321, 323, 329, 341, 345, 363, 369, 371, 375, 393, 405, 411, 413, 429, 441
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Equals (A096787 -1)/2.
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MATHEMATICA
| Select[ Range[ 450], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1, GaussianIntegers -> True] == True &] (from Robert G. Wilson v Jul 11 2004)
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PROG
| (PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=455; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(isprime(p)&&(p%4)==3, print1(n, ", ")); n=k)} - Klaus Brockhaus, Jul 10 2004
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CROSSREFS
| Subsequence (odd numbers) of A096784. See A096787 for the associated primes.
Cf. A060254, A096784, A096785, A096786, A096787, A096676.
Sequence in context: A007962 A061254 A175626 * A050991 A033553 A020192
Adjacent sequences: A096785 A096786 A096787 * A096789 A096790 A096791
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2004
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EXTENSIONS
| Corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 10 2000
I deleted an incorrect comment about Gaussian primes. - Mar 02 2011
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