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 A330927 Numbers k such that both k and k + 1 are Niven numbers. 18
 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 80, 110, 111, 132, 152, 200, 209, 224, 399, 407, 440, 480, 510, 511, 512, 629, 644, 735, 800, 803, 935, 999, 1010, 1011, 1014, 1015, 1016, 1100, 1140, 1160, 1232, 1274, 1304, 1386, 1416, 1455, 1520, 1547, 1651, 1679, 1728, 1853 (list; graph; refs; listen; history; text; internal format)
 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..10000 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 1 is a term since 1 and 1 + 1 = 2 are both Niven numbers. MATHEMATICA nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; nq1 = nivenQ[1]; seq = {}; Do[nq2 = nivenQ[k]; If[nq1 && nq2, AppendTo[seq, k - 1]]; nq1 = nq2, {k, 2, 2000}]; seq PROG (MAGMA) f:=func; a:=[]; for k in [1..2000] do  if forall{m:m in [0..1]|f(k+m)} then Append(~a, k); end if; end for; a; // Marius A. Burtea, Jan 03 2020 CROSSREFS Cf. A005349, A060159, A141769, A154701, A328205, A328209, A328213, A330713, A330928, A330929, A330930, A330931. Sequence in context: A290951 A114800 A079170 * A319387 A076105 A094280 Adjacent sequences:  A330924 A330925 A330926 * A330928 A330929 A330930 KEYWORD nonn,base AUTHOR Amiram Eldar, Jan 03 2020 STATUS approved

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Last modified August 3 21:19 EDT 2021. Contains 346441 sequences. (Running on oeis4.)