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A061885 n + largest triangular number less than or equal to n.

%I A061885 #19 Nov 09 2024 00:43:45
%S A061885 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 A061885 46,47,48,56,57,58,59,60,61,62,63,72,73,74,75,76,77,78,79,80,90,91,92,
%U A061885 93,94,95,96,97,98,99,110,111,112,113,114,115,116,117,118,119,120,132
%N A061885 n + largest triangular number less than or equal to n.
%C A061885 A253607(a(n)) > 0. - _Reinhard Zumkeller_, Jan 05 2015
%C A061885 Also possible values of floor(x*floor(x)) for real x < 1. - _Jianing Song_, Feb 16 2021
%H A061885 Reinhard Zumkeller, <a href="/A061885/b061885.txt">Table of n, a(n) for n = 0..10000</a>
%F A061885 a(n) = n+A057944(n) = 2n-A002262(n) = n+[(sqrt(1+8*n)-1)/2]*[(sqrt(1+8*n)+1)/2]/2.
%F A061885 a(n) = A004201(n+1) - 1. - _Franklin T. Adams-Watters_, Jul 05 2009
%e A061885 a(9) = 9+6 = 15;
%e A061885 a(10) = 10+10 = 20;
%e A061885 a(11) = 11+10 = 21.
%o A061885 (Haskell)
%o A061885 a061885 n = n + a057944 n  -- _Reinhard Zumkeller_, Feb 03 2012
%o A061885 (Python)
%o A061885 from math import comb, isqrt
%o A061885 def A061885(n): return n+comb((m:=isqrt(k:=n+1<<1))+(k>m*(m+1)),2) # _Chai Wah Wu_, Nov 09 2024
%Y A061885 Cf. A060985.
%Y A061885 Cf. A064801 (complement), A253607.
%K A061885 nonn
%O A061885 0,2
%A A061885 _Henry Bottomley_, May 12 2001