

A278814


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


1



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, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..100.


FORMULA

a(n) = ceiling(sqrt(3n+1)).
From Robert Israel, Nov 28 2016: (Start)
G.f.: (1x)^(1)*Sum_{k>=0} (x^(3*k^2)+x^(3*k^2+2*k+1)+x^(3*k^2+4*k+2)).
a(n+1) = a(n)+1 if n is in A032765, otherwise a(n+1) = a(n). (End)


MAPLE

seq(ceil(sqrt(3*k+1)), k=0..100); # Robert Israel, Nov 28 2016


MATHEMATICA

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


PROG

(DERIVE) PROG(y := [], n := 100, LOOP(IF(n = 1, RETURN y), y := ADJOIN(CEILING(SQRT(1 + 3·n)), y), n := n  1))
(PARI) a(n)=sqrtint(3*n)+1 \\ Charles R Greathouse IV, Nov 29 2016
(Python)
from math import isqrt
def A278814(n): return 1+isqrt(3*n) # Chai Wah Wu, Jul 28 2022


CROSSREFS

Cf. A016777, A016789, A016933, A017569, A032765, A058183, A131033, A007494, A051536, A007559.
Sequence in context: A211675 A239683 A132913 * A003160 A060740 A307467
Adjacent sequences: A278811 A278812 A278813 * A278815 A278816 A278817


KEYWORD

nonn,easy,changed


AUTHOR

Mohammad K. Azarian, Nov 28 2016


STATUS

approved



