A079495 - OEIS

%I #5 Sep 24 2013 00:41:40

%S 13,14,16,17,22,23,25,26,31,32,34,35,37,38,39,42,46,47,48,51,58,59,61,

%T 62,64,65,66,69,73,74,75,78,85,86,88,89,91,92,93,96,100,101,102,105,

%U 109,110,111,114,117,126,136,137,138,141,144,153,166,167,169,170,172,173

%N Let b=3. Sum of squares of digits in base b gives 0 (mod b).

%C In base 2 this gives the "Evil Numbers" (cf. A001969) and slope 2. One may conjecture that in base b the asymptotic slope will be b and might suspect asymptotic density 1/b for each result (mod b). For nonprime b larger variations occur and "very big" numbers must be considered to believe in the conjecture (1 million or more...). (Related to A006287, here mod b is considered)

%e 59=(2,0,1,2)_3 thus 2*2+0+1+1=6=0 (mod 3)

%t Ev = Function[{b, x}, vx = IntegerDigits[x, b]; Mod[vx.vx, b]]; Seq = Function[{b, n}, Flatten[Position[Table[Ev[b, k], {k, 1, n}], 0]]]; Seq[3, 1000]

%Y Cf. A001969, A006287, A075311.

%K base,easy,nonn

%O 0,1

%A _Carlos Alves_, Jan 20 2003