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A027434 a(1) = 2; then defined by property that a(n) = smallest number >= a(n-1) such that successive runs have lengths 1,1,2,2,3,3,4,4. 8
2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the sequence of first skipped terms for Beatty sequences in the family alpha = 1+sqrt(n)-sqrt(n-1). - Alisa Ediger, Jul 20 2016

REFERENCES

Sam Speed, An integer sequence (preprint).

LINKS

William A. Tedeschi, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 + floor( sqrt(4*n-3) ).

a(n) = A049068(n) - n.

a(n) = A027709(n)/2. - Tanya Khovanova, Mar 04 2008

a(n) = ceiling(2*sqrt(n)). [Mircea Merca, Feb 07 2012]

a(n) = floor(1+sqrt(n)+sqrt(n-1)). - Alisa Ediger, Jul 20 2016

G.f.: x*(1 + x^(-1/4)*theta_2(x) + theta_3(x))/(2*(1 - x)), where theta_k(x) is the Jacobi theta function. - Ilya Gutkovskiy, Jul 20 2016

MAPLE

A027434:=n->ceil(2*sqrt(n)); seq(A027434(n), n=1..100); # Wesley Ivan Hurt, Mar 01 2014

MATHEMATICA

Table[Ceiling[2*Sqrt[n]], {n, 100}] (* Wesley Ivan Hurt, Mar 01 2014 *)

PROG

(Haskell)

a027434 = (+ 1) . a000196 . (subtract 3) . (* 4)

a027434_list = 2 : concat (map (\x -> replicate (x `div` 2) x) [3..])

-- Reinhard Zumkeller, Mar 23 2013, Nov 22 2011

(PARI) a(n)=sqrtint(4*n-3)+1 \\ Charles R Greathouse IV, Feb 07 2012

CROSSREFS

Sequence in context: A056791 A218767 A261101 * A174697 A176504 A196162

Adjacent sequences:  A027431 A027432 A027433 * A027435 A027436 A027437

KEYWORD

nonn,nice,easy

AUTHOR

Sam Speed (SPEEDS(AT)msci.memphis.edu)

EXTENSIONS

More terms from Courtney Clipp (cclipp(AT)ashland.edu), Dec 08 2004

STATUS

approved

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Last modified February 23 09:49 EST 2018. Contains 299535 sequences. (Running on oeis4.)