A064801 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.