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A262242 Triangular numbers representable as 2^x + 2^y. 3
3, 6, 10, 36, 66, 136, 528, 2080, 8256, 32896, 131328, 524800, 2098176, 8390656, 33558528, 134225920, 536887296, 2147516416, 8590000128, 34359869440, 137439215616, 549756338176, 2199024304128, 8796095119360, 35184376283136, 140737496743936, 562949970198528 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..502

FORMULA

Conjectures from Colin Barker, Sep 16 2015: (Start)

a(n) = 2^(n-5)*(2^n+4) for n>5.

a(n) = 6*a(n-1)-8*a(n-2) for n>7.

G.f.: x*(240*x^6+28*x^5-70*x^4+24*x^3-2*x^2-12*x+3) / ((2*x-1)*(4*x-1)).

(End)

PROG

(Python)

def isTriangular(a):

sr = 1 << (int.bit_length(a) >> 1)

a += a

while a < sr*(sr+1): sr>>=1

b = sr>>1

while b:

s = sr+b

if a >= s*(s+1): sr = s

b>>=1

return (a==sr*(sr+1))

for a in range(1, 200):

for b in range(a):

c = (1<<a) + (1<<b)

if isTriangular(c): print(str(c), end=', ')

CROSSREFS

Cf. A000217, A225390, A226499, A227027, A259745, A259746.

Sequence in context: A356977 A068821 A062100 * A339783 A317361 A048089

Adjacent sequences: A262239 A262240 A262241 * A262243 A262244 A262245

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Sep 15 2015

STATUS

approved

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Last modified December 4 23:46 EST 2022. Contains 358572 sequences. (Running on oeis4.)