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A338705 Products p*q*r of three distinct primes such that s=(p*q) mod r, t=(p*r) mod q and u=(q*r) mod p, and s+t+u are all prime. 2
1885, 4433, 13949, 30709, 39479, 41287, 53627, 55709, 56173, 61957, 63779, 64897, 78217, 79553, 85951, 90097, 92983, 97679, 99517, 101491, 101803, 102131, 103621, 107821, 115915, 119153, 121481, 121619, 128573, 135439, 141349, 141607, 143117, 145337, 146497, 146557, 148219, 152233, 159619, 164083 (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)=13949 is a member because 13949 = 13*29*37 with s = (13*29) mod 37 = 7, t = (13*37) mod 29 = 17, u = (29*37) mod 13 = 7, and 7+17+7 = 31, all prime.

MAPLE

N:= 10^6: # for terms <= N

P:= select(isprime, [seq(i, i=3..floor(sqrt(N)), 2)]):

R:= NULL:

for i from 1 to nops(P) do

  p:= P[i];

  for j from 1 to i-1 do

    q:= P[j];

    if 3*q*p > N then break fi;

    for k from 1 to j-1 do

      r:= P[k];

      if r*q*p > N or r >= p*q then break fi;

      s:= p*q mod r; t:= p*r mod q; u:= q*r mod p;

      if isprime(s) and isprime(t) and isprime(u) and isprime(s+t+u)

          then R:= R, p*q*r

        fi;

od od od:

sort([R]);

MATHEMATICA

Block[{a = {}, nn = 164500}, Do[Do[Do[If[And[Length@ Union[{#1, #2, #3}] == 3, AllTrue[{##}~Join~{#1 + #2 + #3} & @@ {Mod[#1 #2, #3], Mod[#1 #3, #2], Mod[#2 #3, #1]}, PrimeQ]], AppendTo[a, #1 #2 #3]] & @@ {Prime[i], Prime[j], Prime[k]}, {k, j - 1}], {j, i - 1}], {i, PrimePi@ Floor[Sqrt[nn]]}]; TakeWhile[Union@ a, # <= nn &]] (* Michael De Vlieger, Nov 05 2020 *)

CROSSREFS

Subset of A338704.

Sequence in context: A222799 A252111 A259960 * A236613 A190133 A029564

Adjacent sequences:  A338702 A338703 A338704 * A338706 A338707 A338708

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Nov 05 2020

STATUS

approved

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Last modified October 25 06:30 EDT 2021. Contains 348239 sequences. (Running on oeis4.)