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A127491
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Primes which are half of the absolute coefficients [x^2] of the 5-th order polynomials with prime roots as defined in A127489.
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2
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310733, 426871, 15722159, 166492163, 177861107, 270396557, 342955763, 406947461, 1606837039, 1908243773, 2902193117, 3386269021, 5441167877, 6953015807, 7671152921, 10005413687, 10979785673, 14774655421, 16546239937
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The polynomials are of the form (x-prime(i))*(x-prime(i+1))*..*(x-prime(i+4)). The quadratic terms have coefficients which are of the form -sum_{j<k<l} prime(j)*prime(k)*prime(l), summing over all 10 =C(5,3) combinations of products of three distinct primes in the range prime(i) to prime(i+4). If half of the absolute (sign-reversed) coefficient is prime, it is added to the sequence.
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EXAMPLE
| The first contribution is from the 11th polynomial, (x-prime(11)) *(x-prime(12)) *(x-prime(13)) *(x-prime(14)) *(x-prime(15)) = x^5 -199x^4 +15766x^3 -621466x^2 +12185065x -95041567,
where the coefficient of [x^2] is -621466. Its sign-reversed half is 310733, a prime.
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CROSSREFS
| Cf. A127345 - A127351, A006094, A046301 - A046303, A127489, A127490.
Sequence in context: A053849 A116888 A206276 * A205204 A205062 A180461
Adjacent sequences: A127488 A127489 A127490 * A127492 A127493 A127494
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KEYWORD
| nonn,less
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Jan 16 2007
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EXTENSIONS
| Entries replaced to comply with the definition. - R. J. Mathar, Sep 26 2011
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