# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a330930 Showing 1-1 of 1 %I A330930 #14 Mar 17 2024 07:33:30 %S A330930 1,2,3,4,10000095,41441420,124324220,124324221,124324222,207207020, %T A330930 233735070,331531220,350602590,409036350,414414020,467470110, %U A330930 621621020,621621021,621621022,1030302012,1036035020,1051807710,1201800620,1243242020,1243242021,1243242022 %N A330930 Starts of runs of 7 consecutive Niven (or Harshad) numbers (A005349). %C A330930 Cooper and Kennedy proved that there are infinitely many runs of 20 consecutive Niven numbers. Therefore this sequence is infinite. %D A330930 Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110. %H A330930 Amiram Eldar, Table of n, a(n) for n = 1..400 %H A330930 Curtis Cooper and Robert E. Kennedy, On consecutive Niven numbers, Fibonacci Quarterly, Vol. 21, No. 2 (1993), pp. 146-151. %H A330930 Helen G. Grundman, Sequences of consecutive Niven numbers, Fibonacci Quarterly, Vol. 32, No. 2 (1994), pp. 174-175. %H A330930 Wikipedia, Harshad number. %H A330930 Brad Wilson, Construction of 2n consecutive n-Niven numbers, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128. %e A330930 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. %t A330930 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 %Y A330930 Cf. A005349, A060159, A141769, A154701, A330927, A330928, A330929. %K A330930 nonn,base %O A330930 1,2 %A A330930 _Amiram Eldar_, Jan 03 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE