A226499 -id:A226499 - cp's OEIS frontend

A262242 Triangular numbers representable as 2^x + 2^y.

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

Offset: 1

Alex Ratushnyak, Sep 15 2015

nonn

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

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

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<

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)

A262251 Triangular numbers representable as 2^x + 3^y.

Original entry on oeis.org

3, 10, 28, 91

Offset: 1

Alex Ratushnyak, Sep 16 2015

No other terms such that 0 <= x,y < 2000.

No other terms such that 0 <= x,y < 5250. - Michael S. Branicky, Mar 10 2021

			a(1) = 3 = 2^1 + 3^0.
a(4) = 91 = 2^6 + 3^3.

Cf. A225390, A226499, A227027, A259745, A259746, A262242.

Intersection of A000217 and A004050.

isok(t) = {for (k=0, logint(t, 2), my(tt = t - 2^k); if (tt, p = valuation(tt, 3); if (tt == 3^p, return(1))););}
lista(nn) = for (n=1, nn, if (isok(t=n*(n+1)/2), print1(t, ", "))); \\ Michel Marcus, Sep 20 2015

select(x->ispolygonal(x, 3), setbinop(f, [0..20], [0..20])) \\ Michel Marcus, Mar 10 2021

from sympy import integer_nthroot
def auptoexponent(maxexp):
  sums = set(2**x + 3**y for x in range(maxexp) for y in range(maxexp))
  iroots = set(integer_nthroot(2*s, 2)[0] for s in sums)
  return sorted(set(r*(r+1)//2 for r in iroots if r*(r+1)//2 in sums))
print(auptoexponent(500)) # Michael S. Branicky, Mar 10 2021

A262724 Triangular numbers representable as 3^x + y^3.

Original entry on oeis.org

1, 3, 10, 28, 36, 91, 1081, 2278, 2926, 8001, 46665, 5639761, 10911456, 166066200, 341532180, 3137785371, 1647882316985625, 875366737297292691171, 465198187808352499674075441

Offset: 1

Alex Ratushnyak, Sep 28 2015

Any further terms are greater than 10^30. - Charles R Greathouse IV, Oct 02 2015

Cf. A000217, A225390, A226499, A227027, A259745, A259746, A262242, A262251.

list(lim)=my(v=List(),X,t); for(x=0,logint(lim\=1,3), X=3^x; for(y=0, sqrtnint(lim-X,3), if(ispolygonal(t=X+y^3,3), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Sep 28 2015

a(17)-a(19) from Charles R Greathouse IV, Sep 28 2015

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A262242 Triangular numbers representable as 2^x + 2^y.

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A262251 Triangular numbers representable as 2^x + 3^y.

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A262724 Triangular numbers representable as 3^x + y^3.

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