

A326318


Numbers that cannot be written as a difference of 7smooth numbers (A002473).


5



1849, 2309, 2411, 2483, 2507, 2531, 2629, 2711, 2753, 2843, 2851, 2921, 2941, 3139, 3161, 3167, 3181, 3217, 3229, 3251, 3287, 3289, 3293, 3323, 3379, 3481, 3487, 3541, 3601, 3623, 3653, 3697, 3698, 3709, 3737, 3739, 3803, 3827, 3859, 3877, 3901, 3923, 3947
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Terms were found by generating in sequential order the 7smooth numbers up to some limit and collecting the differences. The first 100 candidates k were then proved to be correct by showing that each of the following congruences holds:
<2> + k !== <3, 5, 7> mod 31487336959,
<3> + k !== <2, 5, 7> mod 121328339431,
<2, 3> + k !== <5, 7> mod 5699207989579,
<5> + k !== <2, 3, 7> mod 1206047658673,
<2, 5> + k !== <3, 7> mod 11174958041,
<3, 5> + k !== <2, 7> mod 31487336959,
<7> + k !== <2, 3, 5> mod 1116870318707,
where <a,b,...> represents any element in the subgroup generated by a,b,... of the multiplicative subgroup modulo m. For a discussion iof this method of proof see A308247.


LINKS



EXAMPLE

1849 = A308247(4) cannot be written as the difference of 7smooth numbers. All smaller numbers can; for example, 281 = 2^5*3^2  7, 289 = 2*3*7^2  5, ..., 1847 = 3*5^4  2^2*7.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



