

A327621


Sums of distinct powers of 3 and powers of 4 (greater than 1).


0



3, 4, 7, 9, 12, 13, 16, 19, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 39, 40, 43, 46, 47, 50, 52, 55, 56, 59, 64, 67, 68, 71, 73, 76, 77, 80, 81, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 103, 104, 106, 107, 108, 109, 110, 111, 112
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..64.
P. Erdős, Conjecture about the enumerating function A(x)
S. A. Burr, P. Erdős, R. L. Graham and W. WenChing Li, Complete sequences of sets of integer powers, Acta Arithmetica 77(2) (1996), 133138.
G. Melfi, An additive problem about powers of fixed integers, Rend. Circ. Mat. Palermo 50 (2001), 239246.


FORMULA

For A(x) the enumerating function, Erdős conjectured that A(x) > c*x.
G. Melfi proved that A(x) > x^0.965 for sufficiently large x.


EXAMPLE

40 is in the sequence because 40 = 27 + 9 + 4.


MATHEMATICA

f[b_, m_] := Select[b Range[0, m/b], Max@ IntegerDigits[#, b] < 2 &]; mx=200; Union@ Select[Total /@ Tuples[{f[3, mx], f[4, mx]}], 0 < # < mx &] (* Giovanni Resta, Sep 19 2019 *)


CROSSREFS

Cf. A000244 (powers of 3), A000302 (powers of 4).
Sequence in context: A032729 A035270 A120451 * A060428 A035238 A003136
Adjacent sequences: A327618 A327619 A327620 * A327622 A327623 A327624


KEYWORD

nonn


AUTHOR

Giuseppe Melfi, Sep 19 2019


EXTENSIONS

More terms from Giovanni Resta, Sep 19 2019


STATUS

approved



