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A120864 a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j+k+1)^2 - 4*k = 12*n^2. 2
2, 3, 2, 12, 11, 8, 3, 23, 18, 11, 2, 32, 23, 12, 50, 39, 26, 11, 59, 44, 27, 8, 66, 47, 26, 3, 71, 48, 23, 99, 74, 47, 18, 104, 75, 44, 11, 107, 74, 39, 2, 108, 71, 32, 146, 107, 66, 23, 147, 104, 59, 12, 146, 99, 50, 192, 143, 92, 39, 191, 138, 83, 26, 188, 131, 72, 11, 183 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The k's that match these j's comprise A120865.

REFERENCES

Clark Kimberling, The equation (j+k+1)^2-4*k=Q*n^2 and related dispersions, Journal of Integer Sequences 10 (2007, Article 07.2.7) 1-17.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 3*n^2 - floor(n*sqrt(3))^2.

EXAMPLE

2=3*1-[sqrt(3)]^2

3=3*4-[2*sqrt(3)]^2

2=3*9-[3*sqrt(3)]^2, etc. Moreover,

for n=1, the unique (j,k) is (2,1): (2+1+1)^2-4*1=12*1;

for n=2, the unique (j,k) is (3,4): (3+4+1)^2-4*4=12*4;

for n=3, the unique (j,k) is (2,9): (2+9+1)^2-4*9=12*9.

PROG

(MAGMA) [3*n^2-Floor(n*Sqrt(3))^2: n in [1..70]]; // Vincenzo Librandi, Sep 13 2011

CROSSREFS

Cf. A120865.

Sequence in context: A225787 A012960 A013117 * A173463 A023641 A083775

Adjacent sequences:  A120861 A120862 A120863 * A120865 A120866 A120867

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 09 2006

STATUS

approved

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)