A379591 Numbers k whose base-10 digits can be split into two parts, q and r, with k = (|q-r|)^3.

1000, 456533, 474552, 1000000, 69426531, 1000000000, 1000000000000, 1000000000000000, 1000000000000000000, 1000000000000000000000, 1000000000000000000000000, 1000000000000000000000000000, 1000000000000000000000000000000, 1000000000000000000000000000000000

Offset

1,1

Links

Table of n, a(n) for n=1..14.

Example

1000 = (|10-00|)^3.
456533 = (|456-533|)^3.
1000000 = (|100-0000|)^3.

Maple

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

Prog

(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

Crossrefs

Cf. A102766, A228103.

Sequence in context: A186936 A185747 A234787 * A029799 A029779 A029796

Adjacent sequences: A379588 A379589 A379590 * A379592 A379593 A379594

Keyword

nonn,base

Author

Travis Vasquez, Dec 26 2024

Extensions

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

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

Status

approved