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.

3, 1579, 3967, 14323, 30763, 32189, 41389, 61471, 70117, 74051, 74707, 79691, 95239, 154157, 157181, 157433, 169003, 184321, 215063, 237563, 265271, 300877, 303217, 320741, 326119, 366713, 382241, 392531, 408689, 544723, 572749, 584099, 587219, 615103, 639487, 653561, 674231, 687151, 698483

Offset: 1

Author

J. M. Bergot and Robert Israel, Jul 26 2021

Keywords

• nonn

Comments

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.

Examples

			a(3) = 3967 is a term because 3967, 3989, 4001 are consecutive primes with
3967*3989*4001-(3967+3989+4001) = 63313264406 = 31656632197+31656632209,
3967*3989*4001+(3967+3989+4001) = 63313288320 = 31656644153+31656644167,
31656632197 and 31656632209 are consecutive primes
and 31656644153 and 31656644167 are consecutive primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001043.

Programs

Maple

q:= 2: r:= 3:
R:= NULL: count:= 0:
while count < 40 do
  p:= q; q:= r; r:= nextprime(r);
  s:= p+q+r;
  v:= p*q*r+s;
  t:= prevprime(v/2);
  if nextprime(t)+t <> v then next fi;
  v:= v-2*s;
  t:= prevprime(v/2);
  if nextprime(t)+t = v then
    count:= count+1;
    R:= R, p;
  fi
od:
R;