This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
First few terms of A007950 are 1,3,5,9,11, ... . The first gap of length 1 is between 1 and 3, so a(1) = 1; the first gap of length 2 is between 5 and 9; it has length 3, so a(2) = a(3) = 5.
From _Omar E. Pol_, Aug 29 2018: (Start)
Written as an irregular triangle in which the row lengths are the odd numbers the sequence begins:
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;
...
Row sums give A005917.
Column 1 gives A084849.
Column 2 gives A096376, n >= 1.
Right border gives A000384, n >= 1.
(End)
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
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 *)
With[{nn=20},Take[TakeList[Range[(nn(nn+1))/2],Range[nn]],{1,nn,2}]]//Flatten (* Harvey P. Dale, Feb 10 2023 *)
for(n=1,66,m=sqrtint(n-1);print1(n+m*(m+1),","))
v = List([1..118]); t=3; while (#v>=t, forstep (k=#v\t, 1, -1, listpop(v, k*t);); t*=3;); print (v) \\ Rémy Sigrist, Jan 05 2020
List the natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... Keep the first two numbers 1, 2 and delete the next three numbers 3, 4, 5. Keep the next three numbers 6, 7, 8 and delete the next four numbers 9, 10, 11, 12. And so on.
a048859 n = a048859_list !! (n-1)
a048859_list = f 2 [1..] where
f k xs = us ++ f (k + 1) (drop (k + 1) vs)
where (us, vs) = splitAt k xs
-- Reinhard Zumkeller, May 16 2014
ss[n_]:=Module[{c=n^2+4n+1},Range[c,c+n+1]]; Flatten[Array[ss,10,0]] (* Harvey P. Dale, Sep 10 2014 *)
A = 1:200; A(4:4:end) = 0; A = A(find(A)); A(16:16:end) = 0; A = A(find(A)); A(64:64:end) = 0; A = A(find(A)) % David Wasserman, Apr 28 2004
Start with naturals: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ... Sieve out every 1st number 0 times (do nothing) Sieve out every 2nd number 1 times: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ... Sieve out every 3rd number 2 times: first time: 1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 43, ... second time: 1, 3, 9, 13, 19, 21, 27, 31, 37, 39, 45, 49, 55, 57, 63, ... Sieve out every 4th number 3 times: first time: 1, 3, 9, 19, 21, 27, 37, 39, 45, 55, 57, 63, 73, 75, 81, ... second time: 1, 3, 9, 21, 27, 37, 45, 55, 57, 73, 75, 81, 93, 99, ... third time: 1, 3, 9, 27, 37, 45, 57, 73, 75, 93, 99, 109, 127, 129, ... Sieve out every 5th number 4 times: first time: 1, 3, 9, 27, 45, 57, 73, 75, 99, 109, 127, 129, 153, 165, ... second time: 1, 3, 9, 27, 57, 73, 75, 99, 127, 129, 153, 165, 189, ... third time: 1, 3, 9, 27, 73, 75, 99, 127, 153, 165, 189, 201, 225, ... fourth time: 1, 3, 9, 27, 75, 99, 127, 153, 189, 201, 225, 261, 289, ... Sieve out every 6th number 5 times: ...
def A361423(n): for p in range(n,1,-1): for k in range(p-1): n += (n-1)//(p-1) return n # Bert Dobbelaere, Jul 21 2023
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