A330930 Starts of runs of 7 consecutive Niven (or Harshad) numbers (A005349).

1, 2, 3, 4, 10000095, 41441420, 124324220, 124324221, 124324222, 207207020, 233735070, 331531220, 350602590, 409036350, 414414020, 467470110, 621621020, 621621021, 621621022, 1030302012, 1036035020, 1051807710, 1201800620, 1243242020, 1243242021, 1243242022

Offset

1,2

Comments

Cooper and Kennedy proved that there are infinitely many runs of 20 consecutive Niven numbers. Therefore this sequence is infinite.

References

Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110.

Links

Amiram Eldar, Table of n, a(n) for n = 1..400

Curtis Cooper and Robert E. Kennedy, On consecutive Niven numbers, Fibonacci Quarterly, Vol. 21, No. 2 (1993), pp. 146-151.

Helen G. Grundman, Sequences of consecutive Niven numbers, Fibonacci Quarterly, Vol. 32, No. 2 (1994), pp. 174-175.

Wikipedia, Harshad number.

Brad Wilson, Construction of 2n consecutive n-Niven numbers, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128.

Example

10000095 is a term since 10000095 is divisible by 1 + 0 + 0 + 0 + 0 + 0 + 9 + 5 = 15, 10000096 is divisible by 16, ..., and 10000101 is divisible by 3.

Mathematica

nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; niv = nivenQ /@ Range[7]; seq = {}; Do[niv = Join[Rest[niv], {nivenQ[k]}]; If[And @@ niv, AppendTo[seq, k - 6]], {k, 7, 10^7}]; seq

Crossrefs

Cf. A005349, A060159, A141769, A154701, A330927, A330928, A330929.

Sequence in context: A258107 A307256 A107656 * A024595 A144804 A118308

Adjacent sequences: A330927 A330928 A330929 * A330931 A330932 A330933

Keyword

nonn,base

Author

Amiram Eldar, Jan 03 2020

Status

approved