A267711 Numbers k such that k mod 3 = k mod 5.

0, 1, 2, 15, 16, 17, 30, 31, 32, 45, 46, 47, 60, 61, 62, 75, 76, 77, 90, 91, 92, 105, 106, 107, 120, 121, 122, 135, 136, 137, 150, 151, 152, 165, 166, 167, 180, 181, 182, 195, 196, 197, 210, 211, 212, 225, 226, 227, 240, 241, 242, 255, 256, 257, 270, 271, 272, 285, 286

Offset: 1

Author

Mikk Heidemaa, Jan 19 2016

Keywords

• nonn
• easy

Comments

Periodic differences between the consecutive terms (1,1,13,1,1,13,1,1,13,1,1...).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

Cf. A267540.

Programs

Mathematica

Select[ Range[0, 10000], (Mod[#, 3] == Mod[#, 5]) &]

PARI

lista(nn) = for(n=0, nn, if(n%3 == n%5, print1(n, ", "))); \\ Altug Alkan, Jan 19 2016

PARI

concat(0, Vec(x^2*(1+x+13*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jan 28 2016

Formula

a(n) = (1/3)*(15*n - 12*cos((2*Pi*n)/3) + 4*sqrt(3)*sin((2*Pi*n)/3) - 27).

G.f.: x^2*(13*x^2+x+1) / ((x-1)^2*(x^2+x+1)).

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4. - Colin Barker, Jan 28 2016