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A153053
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Numbers n such that 2*n + 7 is not a prime.
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9
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1, 4, 7, 9, 10, 13, 14, 16, 19, 21, 22, 24, 25, 28, 29, 31, 34, 35, 37, 39, 40, 42, 43, 44, 46, 49, 52, 54, 55, 56, 57, 58, 59, 61, 63, 64, 67, 68, 69, 70, 73, 74, 76, 77, 79, 81, 82, 84, 85, 88, 89, 90, 91, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 112, 114, 115
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OFFSET
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1,2
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COMMENTS
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Let p = prime number, n = (p^2-7)/2 (mod p).
Comment: All numbers of the form 1+3k (k=0,1,2,...) are in this sequence, since 2(3k+1)+7 = 6k+9 is divisible by 3. Moreover, each of these numbers can be extended to an equidistant sequence of length k+1 and step 2k+3: This leads to the triangle T[k,m] = (3k+1)+(2k+3)*m, m=0,...,k, of elements of this sequence, because T[k,m]*2+7 = (2k+3)(2m+3) is never prime. The lines of the triangle end with m=k since the next term T[k,k+1] would be the same as the term in the following line, T[k+1,k]. (The formula T[k,m]=((2k+3)(2m+3)-7)/2 might also explain the comment involving "n=(p^2-7)/2".) [M. F. Hasler, Jun 16 2010]
Solutions of the inequality (2*n+7)'>1, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 27 2012]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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Select[Range[200], !PrimeQ[2# + 7] &] (* Vincenzo Librandi, Nov 21 2012 *)
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PROG
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(PARI) for(n=1, 200, isprime(2*n+7)||print1(n", ")) \\ M. F. Hasler, Jun 16 2010
(MAGMA) [n: n in [1..120] | not IsPrime(2*n + 7)]; // Vincenzo Librandi, Nov 21 2012
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CROSSREFS
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Cf. A105760, A154684.
Sequence in context: A335229 A310939 A175149 * A045752 A266410 A010380
Adjacent sequences: A153050 A153051 A153052 * A153054 A153055 A153056
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Dec 17 2008
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EXTENSIONS
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Checked and extended by M. F. Hasler, Jun 16 2010
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STATUS
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approved
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