%I #15 Mar 16 2026 21:11:57

%S 1,587,28887,49868,228981,158898939,28848999547,76698999868,

%T 493996893887

%N Numbers k that set a new record for A007953(k) - A004164(k).

%C 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.

%C 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.

%H Johannes F. Morgenbesser, <a href="https://www.researchgate.net/publication/228701893_The_sum_of_digits_of_nc">The sum of digits of floor(n^c)</a>, Acta Arithmetica 148 (2011), 367-393.

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

%p R:= 1: count:= 1: m:= 0:

%p for x from 2 while count < 6 do

%p v:= f(x);

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

%p od:

%p R; # _Robert Israel_, Mar 10 2026

%o (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, ", "))))

%Y Cf. A004164, A007953, A064209, A204324.

%K nonn,base,more

%O 1,2

%A _Martin Raab_, Mar 10 2026