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A127346 Primes in A127345. 10
31, 71, 167, 311, 1151, 3119, 4871, 5711, 6791, 14831, 24071, 33911, 60167, 79031, 101159, 106367, 115631, 158231, 235751, 259751, 366791, 402551, 455471, 565919, 635711, 644951, 1124831, 1347971, 1510799, 1547927, 1743419, 1851671, 2048471 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes of the form prime(k)*prime(k+1) + prime(k)*prime(k+2) + prime(k+1)*prime(k+2).
A prime number n is in the sequence if for some k it is the coefficient of x^1 of the polynomial Product_{j=0..2} (x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+2).
LINKS
FORMULA
a(n) = A127345(A204231(n)). - Zak Seidov, Jan 13 2012
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] (* Artur Jasinski, Jan 11 2007 *)
s[li_] := li[[1]]*(li[[2]]+li[[3]])+li[[2]]*li[[3]]; Select[(s[#]&/@Partition[Prime[Range[100]], 3, 1]), PrimeQ] (* Zak Seidov, Jan 13 2012 *)
PROG
(PARI) 1. {m=143; 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=143; 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
(PARI) p=2; q=3; forprime(r=5, 1e3, if(isprime(t=p*q+p*r+q*r), print1(t", ")); p=q; q=r) \\ Charles R Greathouse IV, Jan 13 2012
CROSSREFS
Sequence in context: A050957 A331260 A127345 * A089704 A287609 A210548
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 March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)