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A323047 Numbers that are not the sum of three (or fewer) 3-smooth numbers. 2
431, 485, 509, 565, 637, 671, 719, 725, 727, 862, 887, 935, 941, 943, 959, 967, 970, 1130, 1151, 1175, 1199, 1205, 1274, 1293, 1319, 1342, 1367, 1373, 1391, 1415, 1421, 1423, 1438, 1439, 1445, 1447, 1450, 1453, 1454, 1455, 1481, 1527, 1535, 1559 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers below 431 may be written as a sum of three (or fewer) elements in A003586. These are the first exceptions.

Below 18431 every number can be written as a sum of 4 or fewer 3-smooth numbers, and below 3448733 every number can be written as a sum of 5 or fewer 3-smooth numbers (cf. sequence A018899).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 1000: # for all terms <= N

S:= {seq(seq(2^i*3^j, i=0..ilog2(N/3^j)), j=0..floor(log[3](N)))}:

S2:= select(`<=`, map(t -> op(map(`+`, S, t)), S), N):

S3:= select(`<=`, map(t -> op(map(`+`, S, t)), S2), N):

A:= {$1..N} minus S minus S2 minus S3:

sort(convert(A, list)); # Robert Israel, May 19 2019

MATHEMATICA

f[n_] := Union@ Flatten@ Table[2^a * 3^b, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}];

b=Block[{nn = 2000, s}, s = f[nn]; {0, 1, 2}~Join~Select[Union@ Flatten@ Outer[Plus, s, s, s], # <= nn &]]; Complement[Range[2000], b]

CROSSREFS

Cf. A003586, A018899, A237442, A323046, A323048, A323049, A323050.

Sequence in context: A176387 A160518 A273807 * A046018 A142802 A003548

Adjacent sequences:  A323044 A323045 A323046 * A323048 A323049 A323050

KEYWORD

nonn

AUTHOR

Carlos Alves, Jan 03 2019

STATUS

approved

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)