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A005214 Triangular numbers together with squares (excluding 0). 11
1, 3, 4, 6, 9, 10, 15, 16, 21, 25, 28, 36, 45, 49, 55, 64, 66, 78, 81, 91, 100, 105, 120, 121, 136, 144, 153, 169, 171, 190, 196, 210, 225, 231, 253, 256, 276, 289, 300, 324, 325, 351, 361, 378, 400, 406, 435, 441, 465, 484, 496, 528, 529, 561, 576, 595, 625, 630, 666, 676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A010052(a(n)) + A010054(a(n)) > 0, A010052(a(A193714(n))) = 1, A010054(a(A193715(n))) = 1. - Reinhard Zumkeller, Aug 03 2011

REFERENCES

Hofstadter, D. R., Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, (together with the Fluid Analogies Research Group), NY: Basic Books, 1995. p. 15.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Square Triangular Number

MAPLE

a := proc(n) floor(sqrt(n)): floor(sqrt(n+n)):

`if`(n+n = %*% + % or n = %% * %%, n, NULL) end: # Peter Luschny, May 01 2014

MATHEMATICA

With[{upto=700}, Module[{maxs=Floor[Sqrt[upto]], maxt=Floor[(Sqrt[8upto+1]- 1)/2]}, Union[Join[Range[maxs]^2, Table[(n(n+1))/2, {n, maxt}]]]]] (* Harvey P. Dale, Sep 17 2011 *)

PROG

(Haskell)

a005214 n = a005214_list !! (n-1)

a005214_list = tail $ merge a000290_list a000217_list where

   merge xs'@(x:xs) ys'@(y:ys)

     | x < y     = x : merge xs ys'

     | x == y    = x : merge xs ys

     | otherwise = y : merge xs' ys

-- Reinhard Zumkeller, Aug 03 2011

(PARI) upTo(lim)=vecsort(concat(vector(sqrtint(lim\1), n, n^2), vector(floor(sqrt(2+2*lim)-1/2), n, n*(n+1)/2)), , 8) \\ Charles R Greathouse IV, Aug 04 2011

CROSSREFS

Cf. A054686.

Cf. A001110; union of A000290 and A000217; A117704 (first differences), A193711 (partial sums); A193748, A193749 (partitions into).

Cf. A241241 (subsequence).

Cf. A242401 (complement).

Sequence in context: A034706 A245810 A054686 * A124093 A025061 A037969

Adjacent sequences:  A005211 A005212 A005213 * A005215 A005216 A005217

KEYWORD

nonn,easy

AUTHOR

Russ Cox, Jun 14 1998

STATUS

approved

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Last modified October 1 20:37 EDT 2014. Contains 247522 sequences.