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A007606 Take 1, skip 2, take 3, etc.
(Formerly M3241)
8
1, 4, 5, 6, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 37, 38, 39, 40, 41, 42, 43, 44, 45, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 137, 138 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

List the natural numbers: 1, 2, 3, 4, 5, 6, 7, ... . Keep the first number (1), delete the next two numbers (2, 3), keep the next three numbers (4, 5, 6), delete the next four numbers (7, 8, 9, 10) and so on.

a(A000290(n)) = A000384(n). - Reinhard Zumkeller, Feb 12 2011

A057211(a(n)) = 1. - Reinhard Zumkeller, Dec 30 2011

REFERENCES

C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.

R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

F. Smarandache, Properties of Numbers, 1972.

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000 [From Reinhard Zumkeller, May 13 2009]

C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I.

Index entries for sequences generated by sieves

FORMULA

a(n) = n + m*(m+1) where m = floor(sqrt(n-1)). - Klaus Brockhaus, Mar 26 2004

a(n+1) = a(n) + if n=k^2 then 2*k+1 else 1; a(1) = 1. - Reinhard Zumkeller, May 13 2009

MATHEMATICA

Flatten[ Table[i, {j, 1, 17, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* Robert G. Wilson v, Mar 11 2004 *)

Join[{1}, Flatten[With[{nn=20}, Range[#[[1]], Total[#]]&/@Take[Thread[ {Accumulate[Range[nn]]+1, Range[nn]}], {2, -1, 2}]]]] (* Harvey P. Dale, Jun 23 2013 *)

PROG

(PARI) for(n=1, 66, m=sqrtint(n-1); print1(n+m*(m+1), ", "))

(Haskell)

a007606 n = a007606_list !! (n-1)

a007606_list = takeSkip 1 [1..] where

   takeSkip k xs = take k xs ++ takeSkip (k + 2) (drop (2*k + 1) xs)

-- Reinhard Zumkeller, Feb 12 2011

CROSSREFS

Complement of A007607.

Cf. A007950, A007951, A007952, A048859, A004201.

Sequence in context: A057916 A249853 A162415 * A284513 A047311 A224081

Adjacent sequences:  A007603 A007604 A007605 * A007607 A007608 A007609

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

STATUS

approved

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Last modified February 20 10:10 EST 2018. Contains 299384 sequences. (Running on oeis4.)