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 A330932 Starts of runs of 3 consecutive Niven numbers in base 2 (A049445). 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2. Therefore this sequence is infinite. REFERENCES József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 382. LINKS 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. EXAMPLE 623 is a term since 623, 624 and 625 are all Niven numbers in base 2. MATHEMATICA 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 PROG (Magma) f:=func; 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 CROSSREFS Cf. A049445, A154701, A328210, A328214, A330931, A330933. Sequence in context: A321675 A345556 A345810 * A255086 A158373 A265119 Adjacent sequences: A330929 A330930 A330931 * A330933 A330934 A330935 KEYWORD nonn,base AUTHOR Amiram Eldar, Jan 03 2020 STATUS approved

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Last modified February 5 08:15 EST 2023. Contains 360082 sequences. (Running on oeis4.)