cp's OEIS Frontend

A007606 Take 1, skip 2, take 3, etc.

%I A007606 M3241 #51 Feb 10 2023 19:19:10
%S A007606 1,4,5,6,11,12,13,14,15,22,23,24,25,26,27,28,37,38,39,40,41,42,43,44,
%T A007606 45,56,57,58,59,60,61,62,63,64,65,66,79,80,81,82,83,84,85,86,87,88,89,
%U A007606 90,91,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,137,138
%N A007606 Take 1, skip 2, take 3, etc.
%C A007606 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.
%C A007606 a(A000290(n)) = A000384(n). - _Reinhard Zumkeller_, Feb 12 2011
%C A007606 A057211(a(n)) = 1. - _Reinhard Zumkeller_, Dec 30 2011
%C A007606 Numbers k with the property that the smallest Dyck path of the symmetric representation of sigma(k) has a central valley. (Cf. A237593.) - _Omar E. Pol_, Aug 28 2018
%C A007606 Union of nonzero terms of A000384 and A317304. - _Omar E. Pol_, Aug 29 2018
%C A007606 The values of k such that, in a listing of all congruence classes of positive integers, the k-th congruence class contains k. Here the class r mod m (with r in {1,...,m}) precedes the class r' mod m' (with r' in {1,...,m'}) iff m<m' or r<r'. Cf. A360418. - _James Propp_, Feb 10 2023
%D A007606 C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.
%D A007606 R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.
%D A007606 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007606 F. Smarandache, Properties of Numbers, 1972.
%H A007606 Reinhard Zumkeller, <a href="/A007606/b007606.txt">Table of n, a(n) for n = 1..10000</a>
%H A007606 C. Dumitrescu & V. Seleacu, editors, <a href="http://www.gallup.unm.edu/~smarandache/SNAQINT.txt">Some Notions and Questions in Number Theory, Vol. I</a>.
%H A007606 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A007606 a(n) = n + m*(m+1) where m = floor(sqrt(n-1)). - _Klaus Brockhaus_, Mar 26 2004
%F A007606 a(n+1) = a(n) + if n=k^2 then 2*k+1 else 1; a(1) = 1. - _Reinhard Zumkeller_, May 13 2009
%e A007606 From _Omar E. Pol_, Aug 29 2018: (Start)
%e A007606 Written as an irregular triangle in which the row lengths are the odd numbers the sequence begins:
%e A007606     1;
%e A007606     4,   5,   6;
%e A007606    11,  12,  13,  14,  15;
%e A007606    22,  23,  24,  25,  26,  27,  28;
%e A007606    37,  38,  39,  40,  41,  42,  43,  44,  45;
%e A007606    56,  57,  58,  59,  60,  61,  62 , 63,  64,  65,  66;
%e A007606    79,  80,  81,  82 , 83,  84,  85,  86,  87,  88,  89,  90,  91;
%e A007606   106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120;
%e A007606 ...
%e A007606 Row sums give A005917.
%e A007606 Column 1 gives A084849.
%e A007606 Column 2 gives A096376, n >= 1.
%e A007606 Right border gives A000384, n >= 1.
%e A007606 (End)
%t A007606 Flatten[ Table[i, {j, 1, 17, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (* _Robert G. Wilson v_, Mar 11 2004 *)
%t A007606 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 *)
%t A007606 With[{nn=20},Take[TakeList[Range[(nn(nn+1))/2],Range[nn]],{1,nn,2}]]//Flatten (* _Harvey P. Dale_, Feb 10 2023 *)
%o A007606 (PARI) for(n=1,66,m=sqrtint(n-1);print1(n+m*(m+1),","))
%o A007606 (Haskell)
%o A007606 a007606 n = a007606_list !! (n-1)
%o A007606 a007606_list = takeSkip 1 [1..] where
%o A007606    takeSkip k xs = take k xs ++ takeSkip (k + 2) (drop (2*k + 1) xs)
%o A007606 -- _Reinhard Zumkeller_, Feb 12 2011
%Y A007606 Complement of A007607.
%Y A007606 Cf. A007950, A007951, A007952, A048859, A004201.
%Y A007606 Cf. A000384, A005917, A084849, A096376.
%K A007606 nonn,tabf,nice,easy
%O A007606 1,2
%A A007606 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_