cp's OEIS Frontend

A064801 Take 1, skip 2, take 2, skip 3, take 3, etc.

%I A064801 #43 Jul 20 2024 08:27:40
%S A064801 1,4,5,9,10,11,16,17,18,19,25,26,27,28,29,36,37,38,39,40,41,49,50,51,
%T A064801 52,53,54,55,64,65,66,67,68,69,70,71,81,82,83,84,85,86,87,88,89,100,
%U A064801 101,102,103,104,105,106,107,108,109,121,122,123,124,125,126,127,128
%N A064801 Take 1, skip 2, take 2, skip 3, take 3, etc.
%C A064801 A253607(a(n)) < 0. - _Reinhard Zumkeller_, Jan 05 2015
%C A064801 Integers m such that A000196(m) = A079643(m). - _Firas Melaih_, Dec 10 2020
%C A064801 Also possible values of floor(x*floor(x)) for real x >= 1. - _Jianing Song_, Feb 16 2021
%H A064801 Harry J. Smith, <a href="/A064801/b064801.txt">Table of n, a(n) for n = 1..1000</a>
%F A064801 a(n) = A004202(n) - 1.
%F A064801 Can be interpreted as a table read by rows: T(n,k) = n^2 + k, 0 <= k < n. T(n,k) = 0 iff k > A000196(n); T(n,0) = A000290(n); T(n,1) = A002522(n) for n > 1; T(n,2) = A010000(n) = A059100(n) for n > 2; T(n, n-3) = A014209(n-1) for n > 2; T(n, n-2) = A028552(n) for n > 1; T(n, n-1) = A028387(n-1); T(2*n+1, n) = A001107(n+1). - _Reinhard Zumkeller_, Nov 18 2003
%F A064801 Numbers k such that floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k. - _Rainer Rosenthal_, Jul 19 2024
%p A064801 seq(`if`(floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k, k, NULL), k = 0..2034); # a(1)..a(1000), _Rainer Rosenthal_, Jul 19 2024
%t A064801 a = Table[n, {n, 0, 200} ]; b = {}; Do[a = Drop[a, {1, n} ]; b = Append[b, Take[a, {1, n} ]]; a = Drop[a, {1, n} ], {n, 1, 14} ]; Flatten[b]
%t A064801 Flatten[Table[Range[n^2,n^2+n-1],{n,12}]] (* _Harvey P. Dale_, Dec 18 2015 *)
%o A064801 (PARI) { n=0; for (m=1, 10^9, s=m^2; a=0; for (k=0, m - 1, a=s+k; write("b064801.txt", n++, " ", a); if (n==1000, return)) ) } \\ _Harry J. Smith_, Sep 26 2009
%o A064801 (Haskell)
%o A064801 a064801 n = a064801_list !! (n-1)
%o A064801 a064801_list = f 1 [1..] where
%o A064801    f k xs = us ++ f (k + 1) (drop (k + 1) vs)
%o A064801             where (us, vs) = splitAt k xs
%o A064801 -- _Reinhard Zumkeller_, May 16 2014
%o A064801 (Python)
%o A064801 from math import isqrt  # after _Rainer Rosenthal_
%o A064801 def isA(k: int): return k < ((s:=isqrt(k)) * (s + 1))
%o A064801 print([k for k in range(129) if isA(k)]) # _Peter Luschny_, Jul 19 2024
%Y A064801 Cf. A007606, A004202, A048859.
%Y A064801 Cf. A061885 (complement), A253607.
%Y A064801 Cf. A136272.
%K A064801 easy,nonn
%O A064801 1,2
%A A064801 _Robert G. Wilson v_, Oct 21 2001