|
%I #26 Oct 04 2013 10:11:16
%S 1,9,10,11,19,36,47,63,74,90,91,99,100,101,109,110,111,119,136,147,
%T 163,174,190,191,199,306,316,333,360,361,369,396,407,417,444,470,471,
%U 479,497,603,613,630,631,639,666,693,704,714,740,741,749,777,794,900,901,909,910,911,919,936,947,963,974,990,991,999,1000,1001
%N Numbers n whose sum of digits, sum of square of digits and sum of cube of digits all have the same digital root.
%e a(6)=36 since (first power) 3+6=9; (second power) 3^2+6^2=9+36=45 and 4+5=9; (third power) 3^3+6^3=27+216=243 and 2+4+3=9.
%o (PARI) dr(n) = if (n, (n-1)%9+1); \\ from A010888
%o dsq(n) = if (n, d = digits(n); sum(id = 1, #d, d[id]^2));
%o dcb(n) = if (n, d = digits(n); sum(id = 1, #d, d[id]^3));
%o ok(n) = (dr(n) == dr(dcb(n))) && (dr(n) == dr(dsq(n))); \\ _Michel Marcus_, Sep 24 2013
%Y Cf. A010888 (digital root of n), A007953, A003132, A055012.
%K nonn,base
%O 1,2
%A _Carmine Suriano_, Sep 23 2013
%E Title improved by _Peter Bala_, Sep 25 2013
|
