The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A220689 Triangular numbers generated in A224218. That is, the triangular numbers generated by the operation triangular(i) XOR triangular(i+1) along increasing i. 3
1, 21, 21, 105, 105, 105, 105, 946, 946, 666, 1653, 666, 1378, 946, 1225, 946, 4005, 1378, 4005, 1378, 7381, 1225, 1378, 1653, 2485, 4005, 31125, 4005, 4005, 4005, 2485, 13861, 13861, 5356, 4005, 7381, 5356, 5356, 7381, 4005, 5356, 29161, 12561, 12561, 4186, 4186, 4186, 4186 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A000217(A224218(n)) XOR A000217(A224218(n)+1).
MAPLE
read("transforms") ;
A220689 := proc(n)
i := A224218(n) ;
XORnos(A000217(i), A000217(i+1)) ;
end proc: # R. J. Mathar, Apr 23 2013
MATHEMATICA
nmax = 100;
pmax = 2 nmax^2; (* increase coeff 2 if A224218 is too short *)
A224218 = Join[{0}, Flatten[Position[Partition[Accumulate[Range[pmax]], 2, 1], _?(OddQ[Sqrt[1 + 8 BitXor[#[[1]], #[[2]]]]]&), {1}, Heads -> False]]];
a[n_] := Module[{i}, i = A224218[[n]]; BitXor[PolygonalNumber[i], PolygonalNumber[i+1]]];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Aug 07 2023, after Harvey P. Dale in A224218 *)
PROG
(Python)
def rootTriangular(a):
sr = 1<<33
while a < sr*(sr+1)//2:
sr>>=1
b = sr>>1
while b:
s = sr+b
if a >= s*(s+1)//2:
sr = s
b>>=1
return sr
for i in range(1<<12):
s = (i*(i+1)//2) ^ ((i+1)*(i+2)//2)
t = rootTriangular(s)
if s == t*(t+1)//2:
print(str(s), end=', ')
CROSSREFS
Sequence in context: A371100 A048245 A246034 * A056485 A056475 A219913
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Apr 13 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 12 19:52 EDT 2024. Contains 373360 sequences. (Running on oeis4.)