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 A051533 Numbers that are the sum of two positive triangular numbers. 28
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers n such that 8n+2 is in A085989. - Robert Israel, Mar 06 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 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: A052056 A187974 A193715 * A186151 A184732 A039009 Adjacent sequences:  A051530 A051531 A051532 * A051534 A051535 A051536 KEYWORD easy,nonn,nice AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de) STATUS approved

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Last modified September 18 13:45 EDT 2018. Contains 315130 sequences. (Running on oeis4.)