1,2

The differences between the digit sum of a(n) and the digit sum of a(n)^3, which is always a multiple of 3, for the first few numbers are 0, 3, 6, 9, 12, 15, 18, 21, 30.

The first occurrence of a difference of 24 is found for k=4599599996787. No example of a difference of 27 or larger than 30 is found for k<10^13.

Johannes F. Morgenbesser, The sum of digits of floor(n^c), Acta Arithmetica 148 (2011), 367-393.

49868^3 = 124012611300032, the digit sum of 49868 is 35 while the digit sum of its cube is 26, and 35-26=9.

R:= 1: count:= 1: m:= 0:

for x from 2 while count < 6 do

v:= f(x);

if v > m then m:= v; count:= count+1; R:= R, x; fi

od:

R; # Robert Israel, Mar 10 2026

(PARI) x=-1; forstep(a=0, 10^13, 10, y=sumdigits(a); for(b=1, 9, d=y+b-sumdigits((a+b)^3); if(d>x, x=d; print1(a+b, ", "))))

Cf. A004164, A007953, A064209, A204324.

Sequence in context: A003539 A064209 A113509 * A252387 A186395 A230716

Adjacent sequences: A394105 A394106 A394107 * A394109 A394110 A394111

nonn,base,more

Martin Raab, Mar 10 2026

approved