A323050 Numbers that cannot be written as a sum of two or fewer 7-smooth numbers (A002473).

311, 479, 551, 619, 622, 671, 719, 839, 851, 933, 937, 958, 1102, 1103, 1117, 1151, 1193, 1238, 1244, 1291, 1319, 1342, 1391, 1433, 1437, 1438, 1487, 1499, 1511, 1531, 1553, 1555, 1559, 1619, 1651, 1653, 1667, 1678, 1679, 1697, 1857, 1866, 1871, 1874, 1913, 1916, 1919, 1933, 1937, 1991, 2011, 2013, 2077, 2113, 2117, 2157

Offset

1,1

Comments

Numbers that are not of the form (2^i * 3^j * 5^k * 7^l)*a + (2^m * 3^n * 5^p * 7^q)*b, with i,j,k,m,n,p >= 0, and a,b = 0 or 1. The first number excluded is 311.

These numbers are also included in A323046 and A323049.

Links

Table of n, a(n) for n=1..56.

Mathematica

f[n_] := Union@Flatten@Table[2^a*3^b*5^c*7^d, {a, 0, Log2[n]}, {b, 0, Log[3, n/2^a]}, {c, 0, Log[5, n/(2^a*3^b)]}, {d, 0, Log[7, n/(2^a*3^b*5^c)]}];
b = Block[{nn = 3000, s}, s = f[nn]; {0, 1}~Join~Select[Union@Flatten@Outer[Plus, s, s], # <= nn &]];
Complement[Range[3000], b]

Crossrefs

Similar to A323046 (for 3-smooth) and A323049 (for 5-smooth). Cf. A002473.

Sequence in context: A259221 A142626 A142950 * A104718 A142576 A374103

Adjacent sequences: A323047 A323048 A323049 * A323051 A323052 A323053

Keyword

nonn

Author

Carlos Alves, Jan 03 2019

Status

approved