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n + largest triangular number less than or equal to n.
8

%I #16 Feb 16 2021 20:19:17

%S 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,

%T 46,47,48,56,57,58,59,60,61,62,63,72,73,74,75,76,77,78,79,80,90,91,92,

%U 93,94,95,96,97,98,99,110,111,112,113,114,115,116,117,118,119,120,132

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

%C A253607(a(n)) > 0. - _Reinhard Zumkeller_, Jan 05 2015

%C Also possible values of floor(x*floor(x)) for real x < 1. - _Jianing Song_, Feb 16 2021

%H Reinhard Zumkeller, <a href="/A061885/b061885.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = A004201(n+1) - 1. - _Franklin T. Adams-Watters_, Jul 05 2009

%e a(9) = 9+6 = 15;

%e a(10) = 10+10 = 20;

%e a(11) = 11+10 = 21.

%o (Haskell)

%o a061885 n = n + a057944 n -- _Reinhard Zumkeller_, Feb 03 2012

%Y Cf. A060985.

%Y Cf. A064801 (complement), A253607.

%K nonn

%O 0,2

%A _Henry Bottomley_, May 12 2001