OFFSET
1,1
COMMENTS
Terms were found by generating in sequential order the 7-smooth 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
Esteban Crespi de Valldaura, Table of n, a(n) for n = 1..101
EXAMPLE
1849 = A308247(4) cannot be written as the difference of 7-smooth 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
Esteban Crespi de Valldaura, Jun 26 2019
STATUS
approved