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

Author

Zak Seidov, Nov 08 2015

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Intersection of A014612 and A045920.

Cf. A067813.

Programs

Mathematica

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

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