1,1

1000 = (|10-00|)^3.

456533 = (|456-533|)^3.

1000000 = (|100-0000|)^3.

filter:= proc(x) local m;

for m from 1 to ilog10(x) do

if x = abs((x mod 10^m) - floor(x/10^m))^3 then return true fi

od;

false

end proc:

select(filter, [seq(i^3, i=1..10^7)]); # Robert Israel, Jan 01 2025

(PARI) lista(nn) = my(d, m, q, s, t=1, v=List([])); while(t<nn, t*=10; fordivfactored(t+1, f, if(f[1]>1&&gcd(f[1], (t+1)/f[1])==1, d=[x[1]^x[2]|x<-f[2]~]; forvec(x=vector(#d, i, [0, 1]), s=lift(chinese(chinese(vector(#d, i, Mod((-1)^x[i], d[i]))), Mod(0, (t+1)/f[1]))); q=(s^3-s)/(t+1); if(q>0&&s+q<t, listput(v, s^3))); if(vecmax(f[2][, 1]%4)==1, forvec(x=vector(#d, i, [0, 1]), s=lift(chinese(chinese(vector(#d, i, m=Mod(lift(Mod(-1, f[2][i, 1])^(1/2)), d[i]); for(j=2, f[2][i, 2], m=(m^2-1)/(2*m)); (-1)^x[i]*m)), Mod(0, (t+1)/f[1]))); q=(s^3+s)/(t+1); if(q>=s&&q-s<t, listput(v, s^3))))))); Set(select(x->x<=nn, v)); \\ Jinyuan Wang, Jan 03 2025

Cf. A102766, A228103.

Sequence in context: A186936 A185747 A234787 * A029799 A029779 A029796

Adjacent sequences: A379588 A379589 A379590 * A379592 A379593 A379594

nonn,base

Travis Vasquez, Dec 26 2024

a(11)-a(12) from Michael S. Branicky, Jan 01 2025

a(13)-a(14) from Jinyuan Wang, Jan 03 2025

approved