login
a(n) = ceiling(sqrt(3n+1)).
1

%I #22 Jan 20 2024 11:28:08

%S 1,2,3,4,4,4,5,5,5,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,9,10,10,10,10,10,

%T 10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,13,13,

%U 13,13,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18

%N a(n) = ceiling(sqrt(3n+1)).

%F a(n) = ceiling(sqrt(3n+1)).

%F From _Robert Israel_, Nov 28 2016: (Start)

%F G.f.: (1-x)^(-1)*Sum_{k>=0} (x^(3*k^2)+x^(3*k^2+2*k+1)+x^(3*k^2+4*k+2)).

%F a(n+1) = a(n)+1 if n is in A032765, otherwise a(n+1) = a(n). (End)

%p seq(ceil(sqrt(3*k+1)), k=0..100); # _Robert Israel_, Nov 28 2016

%t Table[Ceiling[Sqrt[3n+1]],{n,0,100}]

%o (Derive) PROG(y := [], n := 100, LOOP(IF(n = -1, RETURN y), y := ADJOIN(CEILING(SQRT(1 + 3·n)), y), n := n - 1))

%o (PARI) a(n)=sqrtint(3*n)+1 \\ _Charles R Greathouse IV_, Nov 29 2016

%o (Python)

%o from math import isqrt

%o def A278814(n): return 1+isqrt(3*n) # _Chai Wah Wu_, Jul 28 2022

%Y Cf. A016777, A016789, A016933, A017569, A032765, A058183, A131033, A007494, A051536, A007559.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Nov 28 2016