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 A141769 Beginning of a run of 4 consecutive Niven (or Harshad) numbers. 26
 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 (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. - Amiram Eldar, Jan 03 2020 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. Eric Weisstein's World of Mathematics, Harshad Number. Wikipedia, Harshad number. Brad Wilson Construction of 2n consecutive n-Niven numbers, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128. FORMULA This A141769 = { A005349(k) | A005349(k+3) = A005349(k)+3 }. - M. F. Hasler, Jan 03 2022 EXAMPLE 510 is in the sequence because 510, 511, 512 and 513 are all Niven numbers. MATHEMATICA 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 *) PROG (Magma) f:=func; 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) print(list(islice(agen(), 40))) # Michael S. Branicky, Mar 17 2024 CROSSREFS Cf. A005349, A330927, A154701, A330928, A330929, A330930, A060159 (start of run of 1, 2, ..., 7, exactly n consecutive Harshad numbers). Cf. A330933, A328211, A328215 (analog for base 2, Zeckendorf- resp. Fibonacci-Niven variants). Sequence in context: A004880 A065666 A240466 * A004891 A037442 A004902 Adjacent sequences: A141766 A141767 A141768 * A141770 A141771 A141772 KEYWORD base,nonn AUTHOR Sergio Pimentel, Sep 15 2008 EXTENSIONS More terms from Amiram Eldar, Jan 03 2020 STATUS approved

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Last modified May 25 06:28 EDT 2024. Contains 372782 sequences. (Running on oeis4.)