A330932 Starts of runs of 3 consecutive Niven numbers in base 2 (A049445).

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

Offset: 1

Author

Amiram Eldar, Jan 03 2020

Keywords

• nonn
• base

Comments

Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2. Therefore this sequence is infinite.

Examples

			623 is a term since 623, 624 and 625 are all Niven numbers in base 2.
		

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.

Crossrefs

Cf. A049445, A154701, A328210, A328214, A330931, A330933.

Programs

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

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