A259504 Numbers n such that n and n+1 are the product of exactly three (not necessarily distinct) primes.

27, 44, 75, 98, 116, 124, 147, 153, 164, 170, 171, 174, 230, 244, 245, 284, 285, 332, 356, 369, 387, 425, 428, 429, 434, 435, 474, 506, 507, 530, 548, 555, 574, 595, 602, 603, 604, 605, 609, 627, 637, 638, 645, 651, 657, 710

Offset

1,1

Comments

Conjecture: this sequence is infinite.

Number of terms < 10^k: 0, 4, 63, 727, 7014, 64556, 585725, 5284711, ... . - Robert G. Wilson v, Nov 09 2015

a(n) = p^3 where p is prime iff p is in intersection of A065508 and A005383. - Altug Alkan, Nov 24 2015

There are 47753279 terms less than 10^9 and 432841730 terms less than 10^10. - Charles R Greathouse IV, Jun 27 2019

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

27=3*3*3, 28=2*2*7.

Mathematica

Select[Range[1000], 3 == PrimeOmega[#] == PrimeOmega[# + 1] &]

Prog

(PARI) forcomposite(n=1, 1e3, if(bigomega(n)==3 && bigomega(n+1)==3, print1(n, ", "))); \\ Altug Alkan, Nov 08 2015
(PARI) list(lim)=my(v=List(), was=1, is); forfactored(n=28, lim\1+1, is=vecsum(n[2][, 2])==3; if(is && was, listput(v, n[1]-1)); was=is); Vec(v) \\ Charles R Greathouse IV, Jun 26 2019

Crossrefs

Intersection of A014612 and A045920.

Cf. A067813.

Sequence in context: A141229 A253919 A357077 * A307373 A121614 A046340

Adjacent sequences: A259501 A259502 A259503 * A259505 A259506 A259507

Keyword

nonn

Author

Zak Seidov, Nov 08 2015

Status

approved