OFFSET
1,2
COMMENTS
A253607(a(n)) < 0. - Reinhard Zumkeller, Jan 05 2015
Also possible values of floor(x*floor(x)) for real x >= 1. - Jianing Song, Feb 16 2021
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = A004202(n) - 1.
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
Numbers k such that floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k. - Rainer Rosenthal, Jul 19 2024
MAPLE
seq(`if`(floor(sqrt(k)) * (floor(sqrt(k)) + 1) > k, k, NULL), k = 0..2034); # a(1)..a(1000), Rainer Rosenthal, Jul 19 2024
MATHEMATICA
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]
Flatten[Table[Range[n^2, n^2+n-1], {n, 12}]] (* Harvey P. Dale, Dec 18 2015 *)
PROG
(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
(Haskell)
a064801 n = a064801_list !! (n-1)
a064801_list = f 1 [1..] where
f k xs = us ++ f (k + 1) (drop (k + 1) vs)
where (us, vs) = splitAt k xs
-- Reinhard Zumkeller, May 16 2014
(Python)
from math import isqrt # after Rainer Rosenthal
def isA(k: int): return k < ((s:=isqrt(k)) * (s + 1))
print([k for k in range(129) if isA(k)]) # Peter Luschny, Jul 19 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Oct 21 2001
STATUS
approved