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A063656 Numbers k such that the truncated square root of k is equal to the rounded square root of k. 6
0, 1, 2, 4, 5, 6, 9, 10, 11, 12, 16, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 36, 37, 38, 39, 40, 41, 42, 49, 50, 51, 52, 53, 54, 55, 56, 64, 65, 66, 67, 68, 69, 70, 71, 72, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also: take 1, skip 0, take 2, skip 1, take 3, skip 2, ...

The union of sets of numbers in closed intervals [k^2,k^2+k], k >= 0, intervals 0 to 1, 1 to 2, 4 to 6, 9 to 12 etc. - J. M. Bergot, Jun 27 2013

Conjecture: the following definition produces a(n) for n >= 1: a(1) = 1; for n > 1, smallest number > a(n-1) satisfying the condition that a(n) is a square if and only if n is a triangular number. - J. Lowell, May 13 2014

Thus a(2) = 2, because 2 is not a triangular number and not a square; a(3) != 3, because 3 is not a square but is a triangular number; a(3) = 4 is OK because 4 is a square and 3 is a triangular number; etc. [Examples supplied by N. J. A. Sloane, May 13 2014]

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Harry J. Smith)

PROG

(PARI) { n=-1; for (m=0, 10^9, if (sqrt(m)%1 < .5, write("b063656.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 27 2009

(Haskell)

a063656 n = a063656_list !! n

a063656_list = f 1 [0..] where

   f k xs = us ++ f (k + 1) (drop (k - 1) vs) where

                    (us, vs) = splitAt k xs

-- Reinhard Zumkeller, Jun 20 2015

CROSSREFS

Cf. A063657, A004201-A004202.

Cf. A128217, A217575.

Sequence in context: A211030 A050015 A153218 * A206907 A076354 A069470

Adjacent sequences:  A063653 A063654 A063655 * A063657 A063658 A063659

KEYWORD

nonn

AUTHOR

Floor van Lamoen, Jul 24 2001

STATUS

approved

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)