OFFSET
1,1
COMMENTS
Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2.
Grundman proved that there are no runs of 5 or more consecutive 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.
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
6222 is a term since 6222, 6223, 6224 and 6225 are all Niven numbers in base 2.
MATHEMATICA
binNivenQ[n_] := Divisible[n, Total @ IntegerDigits[n, 2]]; bin = binNivenQ /@ Range[4]; seq = {}; Do[bin = Join[Rest[bin], {binNivenQ[k]}]; If[And @@ bin, AppendTo[seq, k - 3]], {k, 4, 10^6}]; seq
PROG
(Magma) f:=func<n|n mod &+Intseq(n, 2) eq 0>; a:=[]; for k in [1..1400000] do if forall{m:m in [0..3]|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