A323047 Numbers that are not the sum of three (or fewer) 3-smooth numbers.

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

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