This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A278814 #26 Jun 18 2025 03:16:03
%S A278814 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 A278814 10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,13,13,13,13,13,13,13,
%U A278814 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 A278814 a(n) = ceiling(sqrt(3n+1)).
%F A278814 a(n) = ceiling(sqrt(3n+1)).
%F A278814 From _Robert Israel_, Nov 28 2016: (Start)
%F A278814 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 A278814 a(n+1) = a(n)+1 if n is in A032765, otherwise a(n+1) = a(n). (End)
%F A278814 Sum_{n>=0} (-1)^n/a(n) = log(2) (A002162). - _Amiram Eldar_, Jun 18 2025
%p A278814 seq(ceil(sqrt(3*k+1)), k=0..100); # _Robert Israel_, Nov 28 2016
%t A278814 Table[Ceiling[Sqrt[3n+1]],{n,0,100}]
%o A278814 (Derive) PROG(y := [], n := 100, LOOP(IF(n = -1, RETURN y), y := ADJOIN(CEILING(SQRT(1 + 3·n)), y), n := n - 1))
%o A278814 (PARI) a(n)=sqrtint(3*n)+1 \\ _Charles R Greathouse IV_, Nov 29 2016
%o A278814 (Python)
%o A278814 from math import isqrt
%o A278814 def A278814(n): return 1+isqrt(3*n) # _Chai Wah Wu_, Jul 28 2022
%Y A278814 Cf. A002162, A016777, A016789, A016933, A017569, A032765, A058183, A131033, A007494, A051536, A007559.
%K A278814 nonn,easy
%O A278814 0,2
%A A278814 _Mohammad K. Azarian_, Nov 28 2016