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%I #11 May 23 2024 04:28:04
%S 3,6,10,45,36,28,91,78,66,231,210,120,276,1035,630,378,1431,1378,780,
%T 990,528,496,465,300,820,3321,3240,2080,5356,5253,1275,1225,1176,1128,
%U 4371,4278,4186,5460,4560,11476,11325,2775,666,2016,12880,6555,1596
%N Triangular number pertaining to A081974. a(n) = A081974(n)*A081974(n+1).
%C A subset of A000217. - _R. J. Mathar_, Apr 05 2007
%p isA000217 := proc(n) local t; t := (sqrt(1+8*n)-1)/2 ; type(t,'integer'); end: A081974 := proc(nmax) local a,n,prodset; a := [1,3] ; prodset := {3} ; while nops(a) < nmax do n := 2 ; while n in a or n*op(-1,a) in prodset or isA000217(n*op(-1,a)) = false do n := n+1 ; od ; prodset := prodset union { n*op(-1,a) } ; a := [op(a),n] ; od ; RETURN(a) ; end: A081975 := proc(nmax) local a ; a081974 := A081974(nmax) ; a := [] ; for i from 2 to nops(a081974) do a := [op(a), op(i,a081974)*op(i-1,a081974)] ; od ; RETURN(a) ; end: a := A081975(100) ; # _R. J. Mathar_, Apr 05 2007
%t istriang[n_] := With[{x = Floor[Sqrt[2*n]]}, n == x*(x + 1)/2];
%t nmax = 47;
%t Clear[b, used, tris];
%t b[_] = 0; used[_] = 0; tris[_] = 0; b[1] = 1; used[1] = 1;
%t For[i = 2, i <= nmax+1, i++, f = b[i-1]; j = 2; While[used[j] == 1 || !istriang[f*j] || tris[f*j] == 1, j++]; b[i] = j; used[j] = 1; tris[f*j] = 1];
%t a[n_] := b[n]*b[n + 1];
%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, May 23 2024, after PARI code in A081974 *)
%Y Cf. A081974, A081976, A081977.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Apr 03 2003
%E More terms from _R. J. Mathar_, Apr 05 2007
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