A323048 -id:A323048 - cp's OEIS frontend

A323049 Numbers that are neither 5-smooth nor a sum of two 5-smooth numbers.

71, 119, 142, 191, 211, 213, 223, 238, 239, 284, 299, 311, 319, 355, 357, 359, 367, 373, 382, 397, 419, 422, 426, 431, 446, 461, 463, 467, 473, 476, 478, 479, 497, 523, 529, 547, 551, 553, 559, 568, 569, 571, 573, 583, 589, 595, 598, 599, 607, 613, 617, 619, 622, 623, 638, 639, 659, 669, 671, 703, 709, 710, 713, 714

Offset: 1

Carlos Alves, Jan 03 2019

nonn

Complementary set of (A323048).
Also numbers k such that at least three five-smooth numbers are needed to sum to k. - David A. Corneth, Jan 04 2019
Contains all k == 71 or 119 (mod 120). - Robert Israel, Apr 02 2019

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

Cf. A003586, A051037, A323048.

Similar to A323046 (for 3-smooth numbers).

N:= 1000: # to get all terms <= N
V:= {seq(seq(seq(2^a*3^b*5^c, a = 0 .. floor(log[2](N/3^b/5^c))),b = 0 .. floor(log[3](N/5^c))),c=0..floor(log[5](N)))}:
S:= {$1..N} minus V minus {seq(seq(V[i]+V[j],i=1..j),j=1..nops(V))}:
A:= sort(convert(S,list)): # Robert Israel, Apr 02 2019

f[n_] := Union@Flatten@Table[2^a*3^b*5^c, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a*3^b)]}]; b = Block[{nn = 800, s}, s = f[nn]; {0, 1}~Join~
   Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]];
Complement[Range[800], b]

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

Original entry on oeis.org

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

Carlos Alves, Jan 03 2019

nonn

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).

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

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

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

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]

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A323049 Numbers that are neither 5-smooth nor a sum of two 5-smooth numbers.

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