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A127347 Composites in A127345. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

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]

Select[Total[Times@@@Subsets[#, {2}]]&/@Partition[Prime[ Range[80]], 3, 1], !PrimeQ[#]&] (* Harvey P. Dale, May 27 2012 *)

PROG

(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

CROSSREFS

Cf. A127345, A127346, A127347.

Sequence in context: A285925 A285861 A034282 * A351664 A063877 A204870

Adjacent sequences:  A127344 A127345 A127346 * A127348 A127349 A127350

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jan 11 2007

EXTENSIONS

Edited and extended by Klaus Brockhaus, Jan 21 2007

STATUS

approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)