A063644 Primes with 2 representations: p*q*r - 1 = u*v*w + 1 where p, q, r, u, v and w are primes.

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

Cf. A063639, A063640, A014612.

Sequence in context: A096218 A100590 A046120 * A156782 A347366 A092600

Adjacent sequences: A063641 A063642 A063643 * A063645 A063646 A063647

Keyword

nonn

Author

Reinhard Zumkeller, Jul 21 2001

Status

approved