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A287653 Prime numbers of the form p*q + q*r + r*s with p,q,r,s consecutive primes. 3
127, 1427, 2003, 2713, 7639, 76519, 81703, 139663, 166643, 173777, 349589, 371027, 653357, 696083, 752033, 793699, 883549, 938617, 974713, 1150733, 1176983, 1207223, 1310779, 1675577, 1702577, 1880363, 2715169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 127 = 3*5 + 5*7 + 7*11 =

A000040(2)*A000040(3) + A000040(3)*A000040(4) + A000040(4)*A000040(5) =

A006094(2) + A006094(3) + A006094(4).

MAPLE

N:= 100: # to get a(1) - a(N)

p:= 2: q:= 3: r:= 5: s:= 7:

count:= 0:

while count < N do

  p:= q; q:= r; r:= s; s:= nextprime(s);

  n:= p*q+q*r+r*s;

  if isprime(n) then count:= count+1; A[count]:= n fi

od:

seq(A[i], i=1..N); # Robert Israel, May 29 2017

PROG

(PARI) {p=2; q=3; r=5; s=7; for(k=1, 1000, if(isprime(a=p*q+q*r+r*s),

print1(a", ")); p=q; q=r; r=s; s=nextprime(1+s))}

(Python)

from sympy import nextprime, isprime

A287653_list, pq, qr, rs, s = [], 6, 15, 35, 7

while s <= 10**6:

    n = pq+qr+rs

    if isprime(n):

        A287653_list.append(n)

    t = nextprime(s)

    pq, qr, rs, s = qr, rs, s*t, t # Chai Wah Wu, May 29 2017

CROSSREFS

Cf. A000040 (prime numbers), A006094 (products of 2 successive primes).

Sequence in context: A299718 A300339 A189026 * A258012 A258002 A025598

Adjacent sequences:  A287650 A287651 A287652 * A287654 A287655 A287656

KEYWORD

nonn

AUTHOR

Zak Seidov, May 29 2017

STATUS

approved

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)