A326320 Numbers that cannot be written as a difference of 13-smooth numbers.

35803, 36349, 41299, 43591, 45109, 45583, 53821

Offset: 1

Author

Esteban Crespi de Valldaura, Jun 26 2019

Keywords

• nonn
• more

Comments

Terms were found by generating in ascending order the 13-smooth numbers up to some limit and checking the differences. The first 7 candidates k have been proved true by showing a set of 31 congruences to be impossible (see link below). For a discussion iof this method of proof see A308247.

Examples

			35803 = A308247(6) cannot be written as the difference of 13-smooth numbers. All smaller numbers can; for example, 9007 = 3^2*7*11*13 - 2, 10091 = 2^2*3*5*13^2 - 7^2.
		

Links

• Esteban Crespi de Valldaura, Congruences needed in proof of a(1)..a(7)

Crossrefs

Cf. A080197 (13-smooth numbers).

Cf. numbers not the difference of p-smooth numbers for other values of p: A101082 (p=2), A290365 (p=3), A308456 (p=5), A326318 (p=7), A326319 (p=11).

Cf. A308247.