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 A007607 Skip 1, take 2, skip 3, etc. (Formerly M0821) 10
 2, 3, 7, 8, 9, 10, 16, 17, 18, 19, 20, 21, 29, 30, 31, 32, 33, 34, 35, 36, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers k with the property that the smallest Dyck path of the symmetric representation of sigma(k) has a central peak. (Cf. A237593.) - Omar E. Pol, Aug 28 2018 Union of A317303 and A014105. - Omar E. Pol, Aug 29 2018 REFERENCES 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). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA G.f.: 1/(1-x) * (1/(1-x) + x*Sum_{k>=1} (2k+1)*x^(k*(k+1))). - Ralf Stephan, Mar 03 2004 a(A000290(n)) = A001105(n). - Reinhard Zumkeller, Feb 12 2011 A057211(a(n)) = 0. - Reinhard Zumkeller, Dec 30 2011 a(n) = floor(sqrt(n) + 1/2)^2 + n = A053187(n) + n. - Ridouane Oudra, May 04 2019 EXAMPLE From Omar E. Pol, Aug 29 2018: (Start) Written as an irregular triangle in which the row lengths are the nonzero even numbers the sequence begins: 2, 3; 7, 8, 9, 10; 16, 17, 18, 19, 20, 21; 29, 30, 31, 32, 33, 34, 35, 36; 46, 47, 48, 49, 50, 51, 52, 53, 54, 55; 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78; 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105; 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136; ... Row sums give the nonzero terms of A317297. Column 1 gives A130883, n >= 1. Right border gives A014105, n >= 1. (End) MATHEMATICA Flatten[ Table[i, {j, 2, 16, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* Robert G. Wilson v, Mar 11 2004 *) With[{t=20}, Flatten[Take[TakeList[Range[(t(t+1))/2], Range[t]], {2, -1, 2}]]] (* Harvey P. Dale, Sep 26 2021 *) PROG (Haskell) a007607 n = a007607_list !! (n-1) a007607_list = skipTake 1 [1..] where skipTake k xs = take (k + 1) (drop k xs) ++ skipTake (k + 2) (drop (2*k + 1) xs) -- Reinhard Zumkeller, Feb 12 2011 (PARI) for(m=0, 10, for(n=2*m^2+3*m+2, 2*m^2+5*m+3, print1(n", "))) \\ Charles R Greathouse IV, Feb 12 2011 (Haskell) a007607_list' = f \$ tail \$ scanl (+) 0 [1..] where f (t:t':t'':ts) = [t+1..t'] ++ f (t'':ts) -- Reinhard Zumkeller, Feb 12 2011 CROSSREFS Cf. A063656, A004202, A063657, A007606, A064801, A004202. Complement of A007606. Cf. A014105, A130883, A317297. Similar to A360418. Sequence in context: A284514 A268398 A249587 * A076682 A327224 A231624 Adjacent sequences: A007604 A007605 A007606 * A007608 A007609 A007610 KEYWORD nonn,easy,tabf AUTHOR N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein STATUS approved

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Last modified September 25 20:01 EDT 2023. Contains 365649 sequences. (Running on oeis4.)