A063645 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).

173, 277, 607, 929, 1129, 1181, 1237, 1493, 1549, 1597, 1613, 2011, 2063, 2137, 2423, 2677, 2753, 2767, 2797, 2819, 2851, 2917, 3449, 3533, 3607, 3617, 3727, 4013, 4073, 4177, 4201, 4253, 4493, 4523, 4583, 4691, 4919, 4951, 5119, 5237, 5273, 5393, 5407, 5557

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Example

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

Maple

q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={3}:
select(q, [$2..6000])[];  # Alois P. Heinz, Apr 01 2024

Prog

(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

Crossrefs

Cf. A063641, A063642, A063643, A014612.

Sequence in context: A119567 A142436 A322842 * A142607 A241045 A241046

Adjacent sequences: A063642 A063643 A063644 * A063646 A063647 A063648

Keyword

nonn

Author

Reinhard Zumkeller, Jul 21 2001

Status

approved