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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

Table of n, a(n) for n=1..48.

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

PROG

(Python)

def rootTriangular(a):

    sr = 1L<<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(1L<<16):

        s = (i*(i+1)/2) ^ ((i+1)*(i+2)/2)

        t = rootTriangular(s);

        if s == t*(t+1)/2:

            print str(s)+', ',

CROSSREFS

Cf. A000217, A224218, A224511.

Sequence in context: A022355 A048245 A246034 * A056485 A056475 A219913

Adjacent sequences:  A220686 A220687 A220688 * A220690 A220691 A220692

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Apr 13 2013

STATUS

approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)