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A141769
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Beginning of a run of 4 consecutive Niven (or Harshad) numbers.
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26
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1, 2, 3, 4, 5, 6, 7, 510, 1014, 2022, 3030, 10307, 12102, 12255, 13110, 60398, 61215, 93040, 100302, 101310, 110175, 122415, 127533, 131052, 131053, 196447, 201102, 202110, 220335, 223167, 245725, 255045, 280824, 306015, 311232, 318800, 325600, 372112, 455422
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OFFSET
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1,2
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COMMENTS
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Cooper and Kennedy proved that there are infinitely many runs of 20 consecutive Niven numbers. Therefore this sequence is infinite. - Amiram Eldar, Jan 03 2020
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REFERENCES
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Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110.
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LINKS
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FORMULA
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EXAMPLE
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510 is in the sequence because 510, 511, 512 and 513 are all Niven numbers.
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MATHEMATICA
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nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; niv = nivenQ /@ Range[4]; seq = {}; Do[niv = Join[Rest[niv], {nivenQ[k]}]; If[And @@ niv, AppendTo[seq, k - 3]], {k, 4, 5*10^5}]; seq (* Amiram Eldar, Jan 03 2020 *)
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PROG
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(Magma) f:=func<n|n mod &+Intseq(n) eq 0>; a:=[]; for k in [1..500000] 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
(PARI) {A141769_first( N=50, L=4, a=List())= for(n=1, oo, n+=L; for(m=1, L, n--%sumdigits(n) && next(2)); listput(a, n); N--|| break); a} \\ M. F. Hasler, Jan 03 2022
(Python)
from itertools import count, islice
def agen(): # generator of terms
h1, h2, h3, h4 = 1, 2, 3, 4
while True:
if h4 - h1 == 3: yield h1
h1, h2, h3, h4, = h2, h3, h4, next(k for k in count(h4+1) if k%sum(map(int, str(k))) == 0)
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CROSSREFS
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Cf. A005349, A330927, A154701, A330928, A330929, A330930, A060159 (start of run of 1, 2, ..., 7, exactly n consecutive Harshad numbers).
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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