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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

Zak Seidov, Table of n, a(n) for n = 1..1000

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

Cf. A127345, A127347, A127351, A006094, A002110, A034962, A034965, A082246, A082251, A127340, A127341, A070934, A046301, A046302, A046303, A046324, A046325, A046326, A046327.

Sequence in context: A050957 A331260 A127345 * A089704 A287609 A210548

Adjacent sequences:  A127343 A127344 A127345 * A127347 A127348 A127349

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 October 16 13:06 EDT 2021. Contains 348041 sequences. (Running on oeis4.)