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A340136 Primes p1 such that, with p2, p3, p4 the next three primes, p1*p2+p3*p4+p1, p1*p2+p3*p4+p2, p1*p2+p3*p4+p3 and p1*p2+p3*p4+p4 are all composite. 1
23, 43, 53, 73, 83, 101, 127, 131, 139, 151, 157, 179, 181, 229, 281, 283, 293, 307, 311, 313, 349, 353, 359, 389, 397, 401, 409, 419, 443, 449, 457, 461, 463, 487, 491, 509, 521, 563, 569, 571, 601, 617, 631, 641, 643, 653, 673, 709, 739, 757, 769, 787, 797, 809, 827, 829, 839, 857, 863, 877 (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(3) = 53 is a term because with p1 = 53, p2 = 59, p3 = 61, p4 = 67, we have p1*p2+p3*p4+p1 = 7267, p1*p2+p3*p4+p2 = 7273, p1*p2+p3*p4+p3 = 7275, p1*p2+p3*p4+p4 = 7281, all composite.

MAPLE

p2:=2: p3:= 3: p4:= 5: count:= 0: R:= NULL:

while count < 100 do

  p1:= p2; p2:= p3; p3:= p4; p4:= nextprime(p4);

  w:= p1*p2+p3*p4;

  if not ormap(t -> isprime(t+w), [p1, p2, p3, p4]) then

    count:= count+1; R:= R, p1

  fi

od:

R;

MATHEMATICA

acQ[{a_, b_, c_, d_}]:=AllTrue[a*b+c*d+{a, b, c, d}, CompositeQ]; Select[ Partition[ Prime[ Range[200]], 4, 1], acQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2021 *)

PROG

(PARI) isA340136(p1) = if(!isprime(p1), 0, my(p2=nextprime(1+p1), p3=nextprime(1+p2), p4=nextprime(1+p3), x=((p1*p2)+(p3*p4))); !isprime(x+p1)&&!isprime(x+p2)&&!isprime(x+p3)&&!isprime(x+p4)); \\ Antti Karttunen, Dec 29 2020

CROSSREFS

Cf. A340126.

Sequence in context: A331342 A306085 A037137 * A154530 A156979 A281226

Adjacent sequences:  A340133 A340134 A340135 * A340137 A340138 A340139

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Dec 29 2020

STATUS

approved

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Last modified September 16 16:08 EDT 2021. Contains 347473 sequences. (Running on oeis4.)