A376924 a(n) is the conjectured largest number such that both a(n) and a(n) - n are 7-smooth numbers. a(n) can be less than n. Otherwise, if no such number exists then a(n) = 0.

4375, 8750, 13125, 17500, 21875, 26250, 30625, 35000, 39375, 43750, 3136, 52500, 1728, 61250, 65625, 70000, 5120, 78750, 6144, 87500, 91875, 6272, 2048, 105000, 109375, 3456, 118125, 122500, 2430, 131250, 4000, 140000, 9408, 10240, 153125, 157500, 32805, 12288, 5184, 175000

Offset: 1

Author

Zhicheng Wei, Oct 10 2024

Keywords

• nonn

Examples

			a(31) = 4000 since both 4000 and 4000 - 31 = 3969 are 7-smooth numbers, and there is conjectured no number k larger than 4000 such that both k and k - 31 are 7-smooth numbers.
		

Crossrefs

Cf. A002473.

Programs

PARI

M(v,u,lim)={vecsort(concat(vector(#v, i, my(m=lim\v[i]); v[i]*select(t->t<=m, u))))}
Gen(lim,k)={my(v=[1]); forprime(p=2, k, v=M(v, vector(logint(lim, p)+1, e, p^(e-1)), lim)); v}
lista(n,lim=10^30)={my(v=vector(n), G=Gen(lim,7)); for(i=1, #G, my(t=G[i], k=i+1); while(k<=#G && G[k]-t<=n, v[G[k]-t]=G[k]; k++)); v} \\ Andrew Howroyd, Oct 11 2024

Extensions

a(23) onwards from Andrew Howroyd, Oct 11 2024

Running Andrew Howroyd's PARI program with limit=10^100 does not change the terms in DATA. - Hugo Pfoertner, Oct 13 2024