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Search: id:A127347
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| 551, 791, 1655, 2279, 3935, 8391, 9959, 11639, 13175, 16559, 18383, 20975, 27419, 30191, 32231, 36071, 40511, 45791, 51983, 55199, 64199, 69599, 73911, 84311, 89751, 94679, 112511, 122759, 133419, 145571, 153671, 163775, 169439, 178079
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OFFSET
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1,1
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COMMENT
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Composites of the form prime(k)*prime(k+1)+prime(k)*(prime(k+2)+prime(k+1)*prime(k+2).
A composite number n is in the sequence if for some k it is the coefficient of x^1 of the polynomial Prod_{j=0,2}(x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+2).
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MATHEMATICA
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b = {}; a = {}; Do[If[PrimeQ[Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[a, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[b, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]]], {x, 1, 100}]; Print[a]; Print[b]
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PROGRAM
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(PARI) 1, {m=52; k=2; for(n=1, m, a=sum(i=n, n+k-1, sum(j=i+1, n+k, prime(i)*prime(j))); if(!isprime(a), print1(a, ", ")))} 2. {m=52; k=2; for(n=1, m, a=polcoeff(prod(j=0, k, (x-prime(n+j))), 1); if(!isprime(a), print1(a, ", ")))} - Klaus Brockhaus, Jan 21 2007
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CROSSREFS
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Cf. A127345, A127346, A127347.
Sequence in context: A013538 A141547 A034282 this_sequence A063877 A119897 A014360
Adjacent sequences: A127344 A127345 A127346 this_sequence A127348 A127349 A127350
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Jan 11 2007
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 21 2007
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