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A014368 a(n) = bc, where n = C(b,2)+C(c,1), b>c>=0.

%I A014368 #13 Jul 08 2025 05:37:45
%S A014368 20,21,30,31,32,40,41,42,43,50,51,52,53,54,60,61,62,63,64,65,70,71,72,
%T A014368 73,74,75,76,80,81,82,83,84,85,86,87,90,91,92,93,94,95,96,97,98,100,
%U A014368 101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,1110,120,121,122,123
%N A014368 a(n) = bc, where n = C(b,2)+C(c,1), b>c>=0.
%C A014368 The definition means: write n as the highest possible triangular number plus some nonnegative rest (so b is one plus the index of the greedy inverse of n in A000217), and concatenate the two decimal expansions of b and the rest. - _R. J. Mathar_, May 25 2023
%D A014368 W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge, 1993, p. 158.
%p A014368 invA000217 := proc(n)
%p A014368     local i;
%p A014368     for i from 1 do
%p A014368         if binomial(i+1,2) > n then
%p A014368             return i;
%p A014368         end if;
%p A014368     end do:
%p A014368 end proc:
%p A014368 A014368 := proc(n)
%p A014368     local b,c;
%p A014368     b := invA000217(n) ;
%p A014368     c := n-binomial(b,2) ;
%p A014368     digcatL([b,c]) ;
%p A014368 end proc:
%p A014368 seq(A014368(n),n=1..70) ; # _R. J. Mathar_, May 25 2023
%K A014368 nonn,easy,base
%O A014368 1,1
%A A014368 _N. J. A. Sloane_