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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 (list; graph; refs; listen; history; text; internal format)
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. Wen-Ching Li, Complete sequences of sets of integer powers, Acta Arithmetica 77(2) (1996), 133-138.

G. Melfi, An additive problem about powers of fixed integers, Rend. Circ. Mat. Palermo 50 (2001), 239-246.

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

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Last modified December 1 05:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)