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A226389
Triangular numbers representable as triangular(x)*triangular(y)+1.
1
1, 10, 91, 136, 946, 1711, 1891, 5671, 8911, 10585, 11026, 11935, 13861, 19306, 21736, 26335, 32131, 36856, 44551, 49141, 65341, 107416, 138601, 239086, 305371, 351541, 366796, 459361, 849556, 873181, 933661, 1100386, 1413721, 1516411, 1904176, 2297296, 2467531, 3837835
OFFSET
1,2
COMMENTS
Cases with x=y are included.
The associated indices in A000217 are 1, 4, 13, 16, 43, 58, 61, 106, 133, 145, 148, 154,...
LINKS
EXAMPLE
10 = 3 * 3 + 1,
91 = 6 * 15 + 1,
3837835 = 378 * 10153 + 1.
MAPLE
A000217inv:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end proc:
A000217 := proc(n)
n*(n+1)/2 ;
end proc:
isA226389 := proc(n)
local Tx, Ty;
if n = 1 then
return true;
elif A000217inv(n) >= 0 then
for x from 0 do
Tx := A000217(x) ;
if Tx+1 > n then
return false;
end if;
for y from 0 to x do
Ty := A000217(y) ;
if Tx*Ty+1 >n then
break;
elif Tx*Ty+1 = n then
return true;
end if;
end do:
end do:
else
false;
end if;
end proc:
for n from 0 do
Tn := A000217(n) ;
if isA226389(Tn) then
printf("%d, \n", Tn) ;
end if;
end do: # R. J. Mathar, Jun 06 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Jun 06 2013
STATUS
approved