OFFSET
1,3
COMMENTS
Also, nonnegative m congruent to 0, 1, 3, 6 or 8 (mod 9). The product of any two terms belongs to the sequence and so also a(n)^2, a(n)^3, a(n)^4, etc.
Integers x >= 0 satisfying k*floor(x^2/9) = floor(k*x^2/9) with k >= 0:
k = 0, 1: x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... (A001477);
k = 2: x = 0, 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 15, ... (A060464);
k = 3..8: x = 0, 1, 3, 6, 8, 9, 10, 12, 15, 17, 18, ... (this sequence);
k > 8: x = 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... (A008585).
Primes in sequence: 3, 17, 19, 37, 53, 71, 73, 89, 107, 109, 127, ...
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
FORMULA
G.f.: x^2*(1 + 2*x + 3*x^2 + 2*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-1) + a(n-5) - a(n-6) for n>6.
MATHEMATICA
Select[Range[0, 120], 3 Floor[#^2/9] == Floor[3 #^2/9] &]
Select[Range[0, 120], MemberQ[{0, 1, 3, 6, 8}, Mod[#, 9]] &]
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 3, 6, 8, 9}, 70]
PROG
(Sage) [n for n in (0..120) if 3*floor(n^2/9) == floor(3*n^2/9)]
(Magma) [n: n in [0..120] | 3*Floor(n^2/9) eq Floor(3*n^2/9)]; /* or, by the definition: */ K:=[3..8]; [<k, [n: n in [0..30] | k*Floor(n^2/9) eq Floor(k*n^2/9)]>: k in K];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 06 2015
STATUS
approved