A063656 Numbers k such that the truncated square root of k is equal to the rounded square root of k.

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

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.

Essentially partial sums of A051340.

Sequence in context: A211030 A050015 A153218 * A206907 A076354 A361936

Adjacent sequences: A063653 A063654 A063655 * A063657 A063658 A063659

Keyword

nonn

Author

Floor van Lamoen, Jul 24 2001

Status

approved