OFFSET
1,1
COMMENTS
Numbers k such that 8k+2 is in A085989. - Robert Israel, Mar 06 2017
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Poo-Sung Park, Multiplicative Functions Additive on the Sums of Two Positive Triangular Numbers, Journal of Integer Sequences, Vol. 28 (2025), Article 25.4.8.
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
KEYWORD
easy,nonn,nice
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
STATUS
approved
