A004050 -id:A004050 - cp's OEIS frontend

A226828 Numbers of the form 4^j + 9^k, for j and k >= 0.

2, 5, 10, 13, 17, 25, 65, 73, 82, 85, 97, 145, 257, 265, 337, 730, 733, 745, 793, 985, 1025, 1033, 1105, 1753, 4097, 4105, 4177, 4825, 6562, 6565, 6577, 6625, 6817, 7585, 10657, 16385, 16393, 16465, 17113, 22945, 59050, 59053, 59065, 59113, 59305, 60073, 63145

Offset: 1

T. D. Noe, Jun 19 2013

nonn

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A004050 (2^j + 3^k), A226806-A226832 (cases to 8^j + 9^k).

a = 4; b = 9; mx = 70000; Union[Flatten[Table[a^n + b^m, {m, 0, Log[b, mx]}, {n, 0, Log[a, mx - b^m]}]]]

A226830 Numbers of the form 6^j + 9^k, for j and k >= 0.

Original entry on oeis.org

2, 7, 10, 15, 37, 45, 82, 87, 117, 217, 225, 297, 730, 735, 765, 945, 1297, 1305, 1377, 2025, 6562, 6567, 6597, 6777, 7777, 7785, 7857, 8505, 14337, 46657, 46665, 46737, 47385, 53217, 59050, 59055, 59085, 59265, 60345, 66825, 105705, 279937, 279945, 280017

Offset: 1

T. D. Noe, Jun 19 2013

nonn

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A004050 (2^j + 3^k), A226806-A226832 (cases to 8^j + 9^k).

a = 6; b = 9; mx = 300000; Union[Flatten[Table[a^n + b^m, {m, 0, Log[b, mx]}, {n, 0, Log[a, mx - b^m]}]]]

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

A346676 Numbers expressible as 2^x + 3^y where both x and y are positive integers.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 25, 29, 31, 35, 41, 43, 59, 67, 73, 83, 85, 89, 91, 97, 113, 131, 137, 145, 155, 209, 245, 247, 251, 259, 265, 275, 283, 307, 337, 371, 499, 515, 521, 539, 593, 731, 733, 737, 745, 755, 761, 793, 857, 985, 1027, 1033, 1051, 1105, 1241

Offset: 1

Keith Backman, Jul 28 2021

nonn

All terms have the form 6k +- 1.

Cf. A000079, A000244, A004050.

f(x,y) = 2^x + 3^y;
lista(nn) = select(x->(x<=nn), setbinop(f, [1..logint(nn, 2)], [1..logint(nn, 3)])); \\ Michel Marcus, Jul 29 2021

def aupto(lim):
    s, pow3 = set(), 3
    while pow3 < lim:
        for j in range(1, (lim-pow3).bit_length()):
            s.add(2**j + pow3)
        pow3 *= 3
    return sorted(set(s))
print(aupto(1242)) # Michael S. Branicky, Jul 29 2021

{ A004050 } minus { A000079, A000244 }.

cp's OEIS Frontend

A226828 Numbers of the form 4^j + 9^k, for j and k >= 0.

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A226830 Numbers of the form 6^j + 9^k, for j and k >= 0.

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Mathematica

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

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A346676 Numbers expressible as 2^x + 3^y where both x and y are positive integers.

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Programs

PARI

Python

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