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
Keywords
Examples
5821 is a term: 5821 = A063641(204) = 5823 - 2 = 3*3*647 - 2, 5821 = A063642(225) = 5819 + 2 = 11*23*23 + 2.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
Programs
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Maple
q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={3}: select(q, [$2..6000])[]; # Alois P. Heinz, Apr 01 2024 -
Mathematica
q[p_] := PrimeQ[p] && Union[PrimeOmega /@ {p-2, p+2}] == {3}; Select[Range[2, 6000], q] (* Jean-François Alcover, Jan 13 2025, after Alois P. Heinz *) -
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