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A079495
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Let b=3. Sum of squares of digits in base b gives 0 (mod b).
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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)
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EXAMPLE
| 59=(2,0,1,2)_3 thus 2*2+0+1+1=6=0 (mod 3)
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MATHEMATICA
| 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]
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CROSSREFS
| Cf. A001969, A006287, A075311.
Sequence in context: A054031 A060275 A083984 * A076204 A135024 A173036
Adjacent sequences: A079492 A079493 A079494 * A079496 A079497 A079498
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KEYWORD
| base,easy,nonn
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AUTHOR
| Carlos Alves (cjsalves(AT)gmail.com), Jan 20 2003
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