A063645 - OEIS

%I #15 Apr 01 2024 13:37:42

%S 173,277,607,929,1129,1181,1237,1493,1549,1597,1613,2011,2063,2137,

%T 2423,2677,2753,2767,2797,2819,2851,2917,3449,3533,3607,3617,3727,

%U 4013,4073,4177,4201,4253,4493,4523,4583,4691,4919,4951,5119,5237,5273,5393,5407,5557

%N Primes with two representations: p*q*r - 2 = u*v*w + 2 where p, q, r, u, v and w are primes (not necessarily distinct).

%H Alois P. Heinz, <a href="/A063645/b063645.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harry J. Smith)

%e A063645(50) = 5821: 5821 = A063641(204) = 5823 - 2 = 3*3*647 - 2, 5821 = A063642(225) = 5819 + 2 = 11*23*23 + 2.

%p q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={3}:

%p select(q, [$2..6000])[];  # _Alois P. Heinz_, Apr 01 2024

%o (PARI) { n=0; for (m=2, 10^9, p=prime(m); if (bigomega(p + 2) == 3 && bigomega(p - 2) == 3, write("b063645.txt", n++, " ", p); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 27 2009

%Y Cf. A063641, A063642, A063643, A014612.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 21 2001