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Numbers divisible by 3 or 13.
1

%I #18 Mar 25 2021 04:56:26

%S 3,6,9,12,13,15,18,21,24,26,27,30,33,36,39,42,45,48,51,52,54,57,60,63,

%T 65,66,69,72,75,78,81,84,87,90,91,93,96,99,102,104,105,108,111,114,

%U 117,120,123,126,129,130,132,135,138,141,143,144,147,150,153,156

%N Numbers divisible by 3 or 13.

%C In general, sequences of numbers divisible by primes p and q will have the form a(n+p+q-1) = a(n) + p*q.

%C Union of A008585 and A008595 (0 excluded). - _Michel Marcus_, Oct 16 2013

%C The asymptotic density of this sequence is 5/13. - _Amiram Eldar_, Mar 25 2021

%H Amiram Eldar, <a href="/A230215/b230215.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

%F a(n+15) = a(n) + 39.

%p for n from 1 to 138 do if n mod 3 = 0 or n mod 13= 0 then print(n) fi od

%t Select[Range[200], GCD[#, 39] > 1 &] (* _T. D. Noe_, Oct 15 2013 *)

%t With[{nn=60},Join[3*Range[nn],13*Floor[3/13 Range[nn]]]]//Union//Rest (* _Harvey P. Dale_, May 25 2020 *)

%o (PARI) is(n)=gcd(n,39)>1 \\ _Charles R Greathouse IV_, Dec 11 2013

%Y Complement of A229973.

%Y Cf. A008585, A008595.

%K nonn,easy

%O 1,1

%A _Gary Detlefs_, Oct 11 2013