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A063644
Primes with 2 representations: p*q*r - 1 = u*v*w + 1 where p, q, r, u, v and w are primes.
4
19, 29, 43, 67, 173, 283, 317, 653, 787, 907, 1867, 2083, 2693, 2803, 3413, 3643, 3677, 4253, 4363, 4723, 5443, 5717, 6197, 6547, 6653, 8563, 8573, 9067, 9187, 9403, 9643, 10733, 11443, 11587, 12163, 12917, 13997, 14107, 14683, 15187, 17827
OFFSET
1,1
COMMENTS
Also, primes sandwiched by 3-almost primes. Primes p such that p-+1 are 3-almost primes (A014612). - Zak Seidov, Jul 06 2015
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
EXAMPLE
4723 is a term because 4723 = A063639(168)= 4724 - 1 = 2*2*1181 - 1, and because 4723 = A063640(158)= 4722 + 1 = 2*3*787 + 1.
MATHEMATICA
Select[Prime[Range[3000]], 3 == PrimeOmega[# - 1] == PrimeOmega[# + 1] &] (* Vincenzo Librandi, Jul 07 2015 *)
PROG
(PARI) n=0; default(primelimit, 2000000); for (m=2, 10^9, p=prime(m); if (bigomega(p + 1) == 3 && bigomega(p - 1) == 3, write("b063644.txt", n++, " ", p); if (n==1000, break)) ) \\ Harry J. Smith, Aug 27 2009
(PARI) list(lim)=my(v=List(), u=v, L=(lim+1)\2, t); forprime(p=2, L\2, forprime(q=2, min(p, L\p), listput(u, p*q))); u=Set(u); for(i=2, #u, if(u[i]-u[i-1]==1 && isprime(t=2*u[i]-1), listput(v, t))); Vec(v) \\ Charles R Greathouse IV, Jan 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 21 2001
STATUS
approved