A264043 Numbers n such that n and n+3 are consecutive semiprimes.
6, 22, 35, 46, 62, 74, 82, 115, 155, 166, 206, 259, 262, 295, 323, 355, 358, 362, 395, 466, 478, 482, 502, 511, 559, 562, 583, 586, 611, 623, 626, 671, 703, 718, 731, 734, 746, 755, 763, 799, 835, 838, 862, 866, 886, 895, 914, 923, 955, 979, 982
Offset: 1
Keywords
Examples
6 and 9 are 2nd and 3rd semiprimes, or 6=A001358(2) and 9=A001358(3); 22=A001358(8) and 25=A001358(9).
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,1000}], 4,1],?(#=={1,0,0,1}&)]] (* _Harvey P. Dale, Feb 08 2016 *) -
PARI
for(n=1, 1e3, if(bigomega(n) == 2 && bigomega(n+3) == 2 && bigomega(n+1) !=2 && bigomega(n+2) !=2, print1(n", "))) \\ Altug Alkan, Nov 02 2015
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PARI
is(n)=if(n%4==2, isprime(n/2) && bigomega(n+3)==2 && bigomega(n+1)!=2, n%4==3 && isprime((n+3)/2) && bigomega(n)==2 && bigomega(n+2)!=2) \\ Charles R Greathouse IV, Nov 02 2015
Formula
a(n) >> n log n. - Charles R Greathouse IV, Nov 02 2015