A230215 Numbers divisible by 3 or 13.

3, 6, 9, 12, 13, 15, 18, 21, 24, 26, 27, 30, 33, 36, 39, 42, 45, 48, 51, 52, 54, 57, 60, 63, 65, 66, 69, 72, 75, 78, 81, 84, 87, 90, 91, 93, 96, 99, 102, 104, 105, 108, 111, 114, 117, 120, 123, 126, 129, 130, 132, 135, 138, 141, 143, 144, 147, 150, 153, 156

Offset

1,1

Comments

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

Union of A008585 and A008595 (0 excluded). - Michel Marcus, Oct 16 2013

The asymptotic density of this sequence is 5/13. - Amiram Eldar, Mar 25 2021

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

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

Maple

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

Mathematica

Select[Range[200], GCD[#, 39] > 1 &] (* T. D. Noe, Oct 15 2013 *)
With[{nn=60}, Join[3*Range[nn], 13*Floor[3/13 Range[nn]]]]//Union//Rest (* Harvey P. Dale, May 25 2020 *)

Prog

(PARI) is(n)=gcd(n, 39)>1 \\ Charles R Greathouse IV, Dec 11 2013

Crossrefs

Complement of A229973.

Cf. A008585, A008595.

Sequence in context: A336341 A257220 A092452 * A120688 A102014 A337091

Adjacent sequences: A230212 A230213 A230214 * A230216 A230217 A230218

Keyword

nonn,easy

Author

Gary Detlefs, Oct 11 2013

Status

approved