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 A326318 Numbers that cannot be written as a difference of 7-smooth 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 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 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 Cf. A002473 (7-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), A326319 (p=11), A326320 (p=13). Cf. A308247. Sequence in context: A247724 A236030 A237892 * A115719 A062670 A206468 Adjacent sequences: A326315 A326316 A326317 * A326319 A326320 A326321 KEYWORD nonn AUTHOR Esteban Crespi de Valldaura, Jun 26 2019 STATUS approved

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Last modified December 5 10:40 EST 2023. Contains 367589 sequences. (Running on oeis4.)