The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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<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)
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
KEYWORD
base,nonn
AUTHOR
Sergio Pimentel, Sep 15 2008
EXTENSIONS
More terms from Amiram Eldar, Jan 03 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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