_Carlos Alves (cjsalves(AT)gmail.com), _, Jan 20 2003

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)

base,easy,nonn,new

base,easy,nonn,new

C. Carlos Alves (carloalvcjsalves(AT)netvisaogmail.ptcom), Jan 20 2003

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 non-prime 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)

base,easy,nonn,new

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

13, 14, 16, 17, 22, 23, 25, 26, 31, 32, 34, 35, 37, 38, 39, 42, 46, 47, 48, 51, 58, 59, 61, 62, 64, 65, 66, 69, 73, 74, 75, 78, 85, 86, 88, 89, 91, 92, 93, 96, 100, 101, 102, 105, 109, 110, 111, 114, 117, 126, 136, 137, 138, 141, 144, 153, 166, 167, 169, 170, 172, 173

0,1

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 non-prime 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)

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

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]

Cf. A001969, A006287, A075311.

base,easy,nonn

C. Alves (carloalv(AT)netvisao.pt), Jan 20 2003

approved