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A330932
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Starts of runs of 3 consecutive Niven numbers in base 2 (A049445).
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21
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623, 846, 2358, 4206, 4878, 6127, 6222, 6223, 12438, 16974, 21006, 27070, 31295, 33102, 33103, 35343, 37134, 37630, 37638, 40703, 43263, 45550, 48190, 49230, 52590, 53262, 53263, 56110, 59630, 66198, 66702, 66703, 67878, 69310, 69487, 72655, 74766, 77230, 77958
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OFFSET
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1,1
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COMMENTS
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Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2. Therefore this sequence is infinite.
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REFERENCES
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József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 382.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
Tianxin Cai, On 2-Niven numbers and 3-Niven numbers, Fibonacci Quarterly, Vol. 34, No. 2 (1996), pp. 118-120.
Wikipedia, Harshad number.
Brad Wilson Construction of 2n consecutive n-Niven numbers, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128.
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EXAMPLE
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623 is a term since 623, 624 and 625 are all Niven numbers in base 2.
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MATHEMATICA
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binNivenQ[n_] := Divisible[n, Total @ IntegerDigits[n, 2]]; bin = binNivenQ /@ Range[3]; seq = {}; Do[bin = Join[Rest[bin], {binNivenQ[k]}]; If[And @@ bin, AppendTo[seq, k - 2]], {k, 3, 8*10^4}]; seq
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PROG
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(Magma) f:=func<n|n mod &+Intseq(n, 2) eq 0>; a:=[]; for k in [1..80000] do if forall{m:m in [0..2]|f(k+m)} then Append(~a, k); end if; end for; a; // Marius A. Burtea, Jan 03 2020
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CROSSREFS
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Cf. A049445, A154701, A328210, A328214, A330931, A330933.
Sequence in context: A321675 A345556 A345810 * A255086 A158373 A265119
Adjacent sequences: A330929 A330930 A330931 * A330933 A330934 A330935
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KEYWORD
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nonn,base
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AUTHOR
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Amiram Eldar, Jan 03 2020
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STATUS
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approved
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