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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.

%I A376924 #92 Nov 13 2024 15:03:10
%S A376924 4375,8750,13125,17500,21875,26250,30625,35000,39375,43750,3136,52500,
%T A376924 1728,61250,65625,70000,5120,78750,6144,87500,91875,6272,2048,105000,
%U A376924 109375,3456,118125,122500,2430,131250,4000,140000,9408,10240,153125,157500,32805,12288,5184,175000
%N 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.
%e A376924 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.
%o A376924 (PARI)
%o A376924 M(v,u,lim)={vecsort(concat(vector(#v, i, my(m=lim\v[i]); v[i]*select(t->t<=m, u))))}
%o A376924 Gen(lim,k)={my(v=[1]); forprime(p=2, k, v=M(v, vector(logint(lim, p)+1, e, p^(e-1)), lim)); v}
%o A376924 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
%Y A376924 Cf. A002473.
%K A376924 nonn
%O A376924 1,1
%A A376924 _Zhicheng Wei_, Oct 10 2024
%E A376924 a(23) onwards from _Andrew Howroyd_, Oct 11 2024
%E A376924 Running _Andrew Howroyd_'s PARI program with limit=10^100 does not change the terms in DATA. - _Hugo Pfoertner_, Oct 13 2024