cp's OEIS Frontend

A346653 Numbers p that are the first of three consecutive primes p,q,r such that p*q*r-(p+q+r) and p*q*r+(p+q+r) are both in A001043.

%I A346653 #9 Jul 27 2021 21:18:49
%S A346653 3,1579,3967,14323,30763,32189,41389,61471,70117,74051,74707,79691,
%T A346653 95239,154157,157181,157433,169003,184321,215063,237563,265271,300877,
%U A346653 303217,320741,326119,366713,382241,392531,408689,544723,572749,584099,587219,615103,639487,653561,674231,687151,698483
%N A346653 Numbers p that are the first of three consecutive primes p,q,r such that p*q*r-(p+q+r) and p*q*r+(p+q+r) are both in A001043.
%C A346653 Numbers p that are the first of three consecutive primes p,q,r such that p*q*r-(p+q+r) is the sum of two consecutive primes and p*q*r+(p+q+r) is the sum of two consecutive primes.
%H A346653 Robert Israel, <a href="/A346653/b346653.txt">Table of n, a(n) for n = 1..1000</a>
%e A346653 a(3) = 3967 is a term because 3967, 3989, 4001 are consecutive primes with
%e A346653 3967*3989*4001-(3967+3989+4001) = 63313264406 = 31656632197+31656632209,
%e A346653 3967*3989*4001+(3967+3989+4001) = 63313288320 = 31656644153+31656644167,
%e A346653 31656632197 and 31656632209 are consecutive primes
%e A346653 and 31656644153 and 31656644167 are consecutive primes.
%p A346653 q:= 2: r:= 3:
%p A346653 R:= NULL: count:= 0:
%p A346653 while count < 40 do
%p A346653   p:= q; q:= r; r:= nextprime(r);
%p A346653   s:= p+q+r;
%p A346653   v:= p*q*r+s;
%p A346653   t:= prevprime(v/2);
%p A346653   if nextprime(t)+t <> v then next fi;
%p A346653   v:= v-2*s;
%p A346653   t:= prevprime(v/2);
%p A346653   if nextprime(t)+t = v then
%p A346653     count:= count+1;
%p A346653     R:= R, p;
%p A346653   fi
%p A346653 od:
%p A346653 R;
%Y A346653 Cf. A001043.
%K A346653 nonn
%O A346653 1,1
%A A346653 _J. M. Bergot_ and _Robert Israel_, Jul 26 2021