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..4000
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 10000100 is divisible by 2.
MATHEMATICA
nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; niv = nivenQ /@ Range[6]; seq = {}; Do[niv = Join[Rest[niv], {nivenQ[k]}]; If[And @@ niv, AppendTo[seq, k - 5]], {k, 6, 10^7}]; seq
PROG
(Magma) f:=func<n|n mod &+Intseq(n) eq 0>; a:=[]; for k in [1..30000000] do if forall{m:m in [0..5]|f(k+m)} then Append(~a, k); end if; end for; a; // Marius A. Burtea, Jan 03 2020
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Jan 03 2020
STATUS
approved