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Search: id:A096786
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| A096786 |
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Numbers n such that both n and n+1 are composite numbers that sum up to a Pythagorean prime (i.e. of the form 4k+1). |
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+0
11
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| 8, 14, 20, 26, 44, 48, 50, 54, 56, 68, 74, 86, 90, 98, 114, 116, 120, 128, 134, 140, 146, 158, 168, 174, 176, 186, 194, 200, 204, 216, 224, 230, 254, 260, 278, 284, 288, 296, 300, 308, 320, 326, 338, 350, 354, 380, 384, 386, 398, 404, 410, 414, 426, 428, 440
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Equals (A096785 -1)/2.
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MATHEMATICA
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Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] (from Robert G. Wilson v Jul 11 2004)
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PROGRAM
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(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=465; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(k==n+1&&isprime(p)&&p%4==1, print1(n, ", ")); n=k)} - Klaus Brockhaus, Jul 11 2004
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CROSSREFS
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Subsequence (even numbers) of A096784. See A096785 for the associated primes.
Cf. A060254, A096784, A096785, A096787, A096788, A096675.
Sequence in context: A136798 A091575 A091572 this_sequence A114527 A108058 A063216
Adjacent sequences: A096783 A096784 A096785 this_sequence A096787 A096788 A096789
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2004
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EXTENSIONS
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Corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Rick L. Shepherd (rshepherd2(AT)hotmail.com) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 10 2004
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