A309407 - OEIS

A309407

a(n) = round(sqrt(3*n + 9/4)), with a(0) = 1.

1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 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, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16

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OFFSET

0,2

COMMENTS

Diverges from A046693 at positions in A308766.

For the first 1750 terms, A046693(n)-a(n) is either 0 or 1.

LINKS

Table of n, a(n) for n=0..88.

Ed Pegg Jr, Sparse Rulers.

FORMULA

a(n) = round(sqrt(3*n + 9/4)).

From Michael Chu, Jan 17 2022: (Start)

a(12*k^2 - 6*k) = 6*k - 2 for k>0.

a(12*k^2 + 6*k) = 6*k + 2 for k>0. (End)

MATHEMATICA

Table[If[n == 0, 1, Round[Sqrt[3 n + 9/4]]], {n, 0, 88}]

PROG

(PARI) a(n) = if (n, round(sqrt(3*n + 9/4)), 1); \\ Michel Marcus, Jan 18 2022

(Python)

from math import isqrt

from sympy import integer_nthroot

def A309407(n):

if n == 0: return 1

a, b = integer_nthroot(12*n+9, 2)

return a-(c:=isqrt(3*n+2))-(b&(c&1^1)) # Chai Wah Wu, Jun 19 2024

CROSSREFS

Cf. A046693, A308766, A326499.

Sequence in context: A003057 A239308 A216256 * A046693 A368910 A196376

Adjacent sequences: A309404 A309405 A309406 * A309408 A309409 A309410

KEYWORD

nonn,easy

AUTHOR

Ed Pegg Jr, Jul 29 2019

STATUS

approved