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A259504
Numbers n such that n and n+1 are the product of exactly three (not necessarily distinct) primes.
2
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Nov 08 2015
STATUS
approved