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A051533
Numbers that are the sum of two positive triangular numbers.
31
2, 4, 6, 7, 9, 11, 12, 13, 16, 18, 20, 21, 22, 24, 25, 27, 29, 30, 31, 34, 36, 37, 38, 39, 42, 43, 46, 48, 49, 51, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 69, 70, 72, 73, 76, 79, 81, 83, 84, 87, 88, 90, 91, 92, 93, 94, 97, 99, 100, 101, 102, 106, 108
OFFSET
1,1
COMMENTS
Numbers n such that 8n+2 is in A085989. - Robert Israel, Mar 06 2017
LINKS
Eric Weisstein's World of Mathematics, Fermat's Polygonal Number Theorem
FORMULA
A053603(a(n)) > 0. - Reinhard Zumkeller, Jun 28 2013
A061336(a(n)) = 2. - M. F. Hasler, Mar 06 2017
EXAMPLE
666 is in the sequence because we can write 666 = 435 + 231 = binomial(22,2) + binomial(30,2).
MAPLE
isA051533 := proc(n)
local a, ta;
for a from 1 do
ta := A000217(a) ;
if 2*ta > n then
return false;
end if;
if isA000217(n-ta) then
return true;
end if;
end do:
end proc:
for n from 1 to 200 do
if isA051533(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Dec 16 2015
MATHEMATICA
f[k_] := If[!
Head[Reduce[m (m + 1) + n (n + 1) == 2 k && 0 < m && 0 < n, {m, n},
Integers]] === Symbol, k, 0]; DeleteCases[Table[f[k], {k, 1, 108}], 0] (* Ant King, Nov 22 2010 *)
nn=50; tri=Table[n(n+1)/2, {n, nn}]; Select[Union[Flatten[Table[tri[[i]]+tri[[j]], {i, nn}, {j, i, nn}]]], #<=tri[[-1]] &]
With[{nn=70}, Take[Union[Total/@Tuples[Accumulate[Range[nn]], 2]], nn]] (* Harvey P. Dale, Jul 16 2015 *)
PROG
(Haskell)
a051533 n = a051533_list !! (n-1)
a051533_list = filter ((> 0) . a053603) [1..]
-- Reinhard Zumkeller, Jun 28 2013
(PARI) is(n)=for(k=ceil((sqrt(4*n+1)-1)/2), (sqrt(8*n-7)-1)\2, if(ispolygonal(n-k*(k+1)/2, 3), return(1))); 0 \\ Charles R Greathouse IV, Jun 09 2015
CROSSREFS
Cf. A000217, A020756 (sums of two triangular numbers), A001481 (sums of two squares), A007294, A051611 (complement).
Cf. A061336: minimal number of triangular numbers that sum up to n.
Cf. A085989.
Sequence in context: A187974 A193715 A320474 * A186151 A184732 A039009
KEYWORD
easy,nonn,nice
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
STATUS
approved