A061885 - OEIS

A061885

n + largest triangular number less than or equal to n.

0, 2, 3, 6, 7, 8, 12, 13, 14, 15, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 56, 57, 58, 59, 60, 61, 62, 63, 72, 73, 74, 75, 76, 77, 78, 79, 80, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 132

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

OFFSET

0,2

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

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = n+A057944(n) = 2n-A002262(n) = n+[(sqrt(1+8*n)-1)/2]*[(sqrt(1+8*n)+1)/2]/2.

a(n) = A004201(n+1) - 1. - Franklin T. Adams-Watters, Jul 05 2009

EXAMPLE

a(9) = 9+6 = 15;

a(10) = 10+10 = 20;

a(11) = 11+10 = 21.

PROG

(Haskell)

a061885 n = n + a057944 n -- Reinhard Zumkeller, Feb 03 2012

(Python)

from math import comb, isqrt

def A061885(n): return n+comb((m:=isqrt(k:=n+1<<1))+(k>m*(m+1)), 2) # Chai Wah Wu, Nov 09 2024

CROSSREFS

Cf. A060985.

Cf. A064801 (complement), A253607.

Sequence in context: A327176 A065193 A116047 * A138683 A072426 A189137

Adjacent sequences: A061882 A061883 A061884 * A061886 A061887 A061888

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 12 2001

STATUS

approved

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