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

1, 4, 5, 9, 10, 11, 16, 17, 18, 19, 25, 26, 27, 28, 29, 36, 37, 38, 39, 40, 41, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 69, 70, 71, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 121, 122, 123, 124, 125, 126, 127, 128

Offset

1,2

Comments

A253607(a(n)) < 0. - Reinhard Zumkeller, Jan 05 2015

Integers m such that A000196(m) = A079643(m). - Firas Melaih, Dec 10 2020

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

Cf. A007606, A004202, A048859.

Cf. A061885 (complement), A253607.

Cf. A136272.

Sequence in context: A115915 A007536 A209887 * A109825 A327175 A193259

Adjacent sequences: A064798 A064799 A064800 * A064802 A064803 A064804

Keyword

easy,nonn

Author

Robert G. Wilson v, Oct 21 2001

Status

approved