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Search: id:A111434
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| A111434 |
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Numbers n such that the sums of the digits of n, n^2 and n^3 coincide. |
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+0
2
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| 0, 1, 10, 100, 468, 585, 1000, 4680, 5850, 5851, 5868, 10000, 28845, 46800, 58500, 58510, 58680, 58968, 100000, 288450, 468000, 585000, 585100, 586800, 589680, 1000000, 2884500, 4680000, 5850000, 5851000, 5868000, 5896800, 10000000
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The sequence is clearly infinite, since we can add trailing zeros. Is the subset of values not ending in 0 infinite too (see A114135)?
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EXAMPLE
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468 is in the sequence since 468^2=219024and 468^3=102503232 and we have 18=4+6+8=2+1+9+0+2+4=1+0+2+5+0+3+2+3+2.
5851 is in the sequence because 5851, 34234201 (= 5851^2) and 200304310051 (=5851^3) all have digital sum 19.
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MAPLE
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s:=proc(n) local nn: nn:=convert(n, base, 10): sum(nn[j], j=1..nops(nn)): end: a:=proc(n) if s(n)=s(n^2) and s(n)=s(n^3) then n else fi end: seq(a(n), n=0..1000000); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 13 2006
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MATHEMATICA
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SumOfDig[n_]:=Apply[Plus, IntegerDigits[n]]; Do[s=SumOfDig[n]; If[s==SumOfDig[n^2] && s==SumOfDig[n^3], Print[n]], {n, 10^6}]
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CROSSREFS
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Cf. A058369, A070276.
Sequence in context: A134556 A060522 A086115 this_sequence A092707 A136876 A136858
Adjacent sequences: A111431 A111432 A111433 this_sequence A111435 A111436 A111437
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KEYWORD
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base,nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Nov 21 2005
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