A330927 -id:A330927 - cp's OEIS frontend

A005349 Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200, 201, 204

Offset: 1

N. J. A. Sloane, Robert G. Wilson v

Both spellings, "Harshad" or "harshad", are in use. It is a Sanskrit word, and in Sanskrit there is no distinction between upper- and lower-case letters. - N. J. A. Sloane, Jan 04 2022
z-Niven numbers are numbers n which are divisible by (A*s(n) + B) where A, B are integers and s(n) is sum of digits of n. Niven numbers have A = 1, B = 0. - Ctibor O. Zizka, Feb 23 2008
A070635(a(n)) = 0. A038186 is a subsequence. - Reinhard Zumkeller, Mar 10 2008
A049445 is a subsequence of this sequence. - Ctibor O. Zizka, Sep 06 2010
Complement of A065877; A188641(a(n)) = 1; A070635(a(n)) = 0. - Reinhard Zumkeller, Apr 07 2011
A001101, the Moran numbers, are a subsequence. - Reinhard Zumkeller, Jun 16 2011
A140866 gives the number of terms <= 10^k. - Robert G. Wilson v, Oct 16 2012
The asymptotic density of this sequence is 0 (Cooper and Kennedy, 1984). - Amiram Eldar, Jul 10 2020
From Amiram Eldar, Oct 02 2023: (Start)
Named "Harshad numbers" by the Indian recreational mathematician Dattatreya Ramchandra Kaprekar (1905-1986) in 1955. The meaning of the word is "giving joy" in Sanskrit.
Named "Niven numbers" by Kennedy et al. (1980) after the Canadian-American mathematician Ivan Morton Niven (1915-1999). During a lecture given at the 5th Annual Miami University Conference on Number Theory in 1977, Niven mentioned a question of finding a number that equals twice the sum of its digits, which appeared in the children's pages of a newspaper. (End)

			195 is a term of the sequence because it is divisible by 15 (= 1 + 9 + 5).

Paul Dahlenberg and T. Edgar, Consecutive factorial base Niven numbers, Fib. Q., 56:2 (2018), 163-166.
D. R. Kaprekar, Multidigital Numbers, Scripta Math., Vol. 21 (1955), p. 27.
Robert E. Kennedy and Curtis N. Cooper, On the natural density of the Niven numbers, Abstract 816-11-219, Abstracts Amer. Math. Soc., 6 (1985), 17.
Robert E. Kennedy, Terry A. Goodman, and Clarence H. Best, Mathematical Discovery and Niven Numbers, The MATYC Journal, Vol. 14, No. 1 (1980), pp. 21-25.
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 381.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 171.

N. J. A. Sloane, Table of n, a(n) for n = 1..11872 (all a(n) <= 100000)
Bob Albrecht, Don Albers, and Jim Conlan, Problem #22 Two-digit Niven numbers, Programming Problems, Recreational Computing Magazine, Vol. 9, No. 1, Issue 46 (1980), p. 59.
Curtis N. Cooper and Robert E. Kennedy, On an asymptotic formula for the Niven numbers, International Journal of Mathematics and Mathematical Sciences, Vol. 8, No. 3 (1985), pp. 537-543.
Curtis N. Cooper and Robert E. Kennedy, Chebyshev's inequality and natural density, Amer. Math. Monthly 96 (1989), no. 2, 118-124.
Paul Dalenberg and Tom Edgar, Consecutive factorial base Niven numbers, Fibonacci Quart. (2018) Vol. 56, No. 2, 163-166.
Jean-Marie De Koninck and Nicolas Doyon, Large and Small Gaps Between Consecutive Niven Numbers, J. Integer Seqs., Vol. 6, 2003, Article 03.2.5.
Nicolas Doyon, Les fascinants nombres de Niven, Thèse de la Faculté des Sciences et de Génie de l'Université Laval, Québec, Novembre 2006 (in French).
Ömer Eğecioğlu and Bünyamin Şahin, On twin EP numbers, Transact. Comb. (2025) Vol. 14, Iss. 4, Art. No. 4, 261-270. See p. 262.
Richard K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20.
Richard K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
Robert E. Kennedy, Digital sums, Niven numbers, and natural density, Crux Mathematicorum, Vol. 8 (1982), pp. 131-135.
Robert E. Kennedy and Curtis N. Cooper, On the natural density of the Niven numbers, The College Mathematics Journal, Vol. 15, No. 4 (Sep., 1984), pp. 309-312.
Project Euler, Harshad Numbers: Problem 387.
Terry Trotter, Niven Numbers for Fun and Profit. [archived page]
Gérard Villemin, Nombres de Harshad (French).
Elaine E. Visitacion, Renalyn T. Boado, Mary Ann V. Doria, and Eduard M. Albay, On Harshad Number, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 134-138. [archived]
Eric Weisstein's World of Mathematics, Digit and Harshad Numbers.
Wikipedia, Harshad number.

Cf. A001101, A007602, A007953, A028834, A038186, A049445, A052018, A052019, A052020, A052021, A052022, A065877, A070635, A113315, A188641.
Cf. A001102 (a subsequence).
Cf. A118363 (for factorial-base analog).
Cf. A330927, A154701, A141769, A330928, A330929, A330930 (start of runs of 2, 3, ..., 7 consecutive Niven numbers).

Filtered([1..230],n-> n mod List(List([1..n],ListOfDigits),Sum)[n]=0); # Muniru A Asiru

a005349 n = a005349_list !! (n-1)
a005349_list = filter ((== 0) . a070635) [1..]
-- Reinhard Zumkeller, Aug 17 2011, Apr 07 2011

[n: n in [1..250] | n mod &+Intseq(n) eq 0];  // Bruno Berselli, May 28 2011

[n: n in [1..250] | IsIntegral(n/&+Intseq(n))];  // Bruno Berselli, Feb 09 2016

s:=proc(n) local N:N:=convert(n,base,10):sum(N[j],j=1..nops(N)) end:p:=proc(n) if floor(n/s(n))=n/s(n) then n else fi end: seq(p(n),n=1..210); # Emeric Deutsch

harshadQ[n_] := Mod[n, Plus @@ IntegerDigits@ n] == 0; Select[ Range[1000], harshadQ] (* Alonso del Arte, Aug 04 2004 and modified by Robert G. Wilson v, Oct 16 2012 *)
Select[Range[300],Divisible[#,Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 07 2015 *)

is(n)=n%sumdigits(n)==0 \\ Charles R Greathouse IV, Oct 16 2012

A005349 = [n for n in range(1,10**6) if not n % sum([int(d) for d in str(n)])] # Chai Wah Wu, Aug 22 2014

[n for n in (1..10^4) if sum(n.digits(base=10)).divides(n)] # Freddy Barrera, Jul 27 2018

A154701 Numbers k such that k, k + 1 and k + 2 are 3 consecutive Harshad numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 110, 510, 511, 1010, 1014, 1015, 2022, 2023, 2464, 3030, 3031, 4912, 5054, 5831, 7360, 8203, 9854, 10010, 10094, 10307, 10308, 11645, 12102, 12103, 12255, 12256, 13110, 13111, 13116, 13880, 14704, 15134, 17152, 17575, 18238, 19600, 19682

Offset: 1

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 14 2009, Jan 15 2009

Harshad numbers are also known as Niven numbers.

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

			110 is a term since 110 is divisible by 1 + 1 + 0 = 2, 111 is divisible by 1 + 1 + 1 = 3, and 112 is divisible by 1 + 1 + 2 = 4.

Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110.

Robert Israel, 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.

A subset of A005349.

Cf. A060159, A141769, A328210, A328214, A330927, A330928, A330929, A330930, A330932.

#include 
#include 
int is_harshad(int n){
  int i,j,count=0;
  i=n;
  while(i>0){
    count=count+i%10;
    i=i/10;
  }
  return n%count==0?1:0;
}
main(){
  int k;
  clrscr();
  for(k=1;k<=30000;k++)
    if(is_harshad(k)&&is_harshad(k+1)&&is_harshad(k+2))
      printf("%d,",k);
  getch();
  return 0;
}

f:=func; a:=[]; for k in [1..20000] do  if forall{m:m in [0..2]|f(k+m)} then Append(~a,k); end if; end for; a; // Marius A. Burtea, Jan 03 2020

Res:= NULL: count:= 0:
state:= 1:
L:= [1]:
for n from 2 while count < 100 do
  L[1]:=L[1]+1;
  for k from 1 while L[k]=10 do L[k]:= 0;
    if k = nops(L) then L:= [0$nops(L),1]; break
    else L[k+1]:= L[k+1]+1 fi
  od:
  s:= convert(L,`+`);
  if n mod s = 0 then
     state:= min(state+1,3);
     if state = 3 then count:= count+1; Res:= Res, n-2; fi
  else state:= 0
  fi
od:
Res; # Robert Israel, Feb 01 2019

nivenQ[n_] := Divisible[n, Total @ IntegerDigits[n]]; niv = nivenQ /@ Range[3]; seq = {}; Do[niv = Join[Rest[niv], {nivenQ[k]}]; If[And @@ niv, AppendTo[seq, k - 2]], {k, 3, 2*10^4}]; seq (* Amiram Eldar, Jan 03 2020 *)

from itertools import count, islice
def agen(): # generator of terms
    h1, h2, h3 = 1, 2, 3
    while True:
        if h3 - h1 == 2: yield h1
        h1, h2, h3 = h2, h3, next(k for k in count(h3+1) if k%sum(map(int, str(k))) == 0)
print(list(islice(agen(), 45))) # Michael S. Branicky, Mar 17 2024

A330931 Numbers k such that both k and k + 1 are Niven numbers in base 2 (A049445).

Original entry on oeis.org

1, 20, 68, 80, 115, 155, 184, 204, 260, 272, 284, 320, 344, 355, 395, 404, 424, 464, 555, 564, 595, 623, 624, 636, 664, 675, 804, 835, 846, 847, 864, 875, 888, 904, 972, 1028, 1040, 1075, 1088, 1124, 1164, 1182, 1211, 1224, 1239, 1266, 1280, 1304, 1315, 1424

Offset: 1

Amiram Eldar, Jan 03 2020

Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2. Therefore this sequence is infinite.

			20 is a term since 20 and 20 + 1 = 21 are both Niven numbers in base 2.

József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 382.

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.
Wikipedia, Harshad number.
Brad Wilson, Construction of 2n consecutive n-Niven numbers, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128.

Cf. A049445, A328205, A328209, A328213, A330713, A330927, A330932, A330933.

f:=func; a:=[]; for k in [1..1500] 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

binNivenQ[n_] := Divisible[n, Total @ IntegerDigits[n, 2]]; bnq1 = binNivenQ[1]; seq = {}; Do[bnq2 = binNivenQ[k]; If[bnq1 && bnq2, AppendTo[seq, k - 1]]; bnq1 = bnq2, {k, 2, 10^4}]; seq

def sbd(n): return sum(map(int, str(bin(n)[2:])))
def niv2(n): return n%sbd(n) == 0
def aupto(nn): return [k for k in range(1, nn+1) if niv2(k) and niv2(k+1)]
print(aupto(1424)) # Michael S. Branicky, Jan 20 2021

A141769 Beginning of a run of 4 consecutive Niven (or Harshad) numbers.

Original entry on oeis.org

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

Offset: 1

Sergio Pimentel, Sep 15 2008

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

			510 is in the sequence because 510, 511, 512 and 513 are all Niven numbers.

Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 36, entry 110.

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.

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).

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

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 *)

{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

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

This A141769 = { A005349(k) | A005349(k+3) = A005349(k)+3 }. - M. F. Hasler, Jan 03 2022

More terms from Amiram Eldar, Jan 03 2020

A331086 Positive numbers k such that k and k + 1 are both negaFibonacci-Niven numbers (A331085).

Original entry on oeis.org

1, 4, 5, 9, 12, 13, 26, 68, 86, 87, 88, 89, 93, 99, 155, 176, 177, 183, 195, 212, 230, 231, 232, 233, 237, 243, 255, 320, 321, 327, 384, 395, 411, 415, 424, 464, 465, 471, 475, 484, 515, 544, 575, 591, 602, 644, 655, 656, 744, 824, 875, 894, 924, 1043, 1115, 1127

Offset: 1

Amiram Eldar, Jan 08 2020

Fibonacci numbers F(6*k - 1) and F(6*k) are terms.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A328209, A328213, A330927, A330931, A331085.

ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
negFibQ[n_] := Divisible[n, negaFibTermsNum[n]];
nConsec = 2; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq

A333427 Numbers k such that k and k+1 are both primorial base Niven numbers (A333426).

Original entry on oeis.org

1, 8, 24, 32, 44, 64, 65, 132, 212, 224, 244, 245, 296, 368, 424, 425, 468, 560, 656, 720, 728, 737, 869, 1056, 1088, 1416, 1572, 1728, 2100, 2312, 2324, 2344, 2345, 2524, 2525, 2568, 2600, 2672, 2820, 2960, 3032, 3132, 3156, 3200, 3288, 3392, 3444, 4096, 4424

Offset: 1

Amiram Eldar, Mar 20 2020

nonn

			1 is a term since 1 and 2 are both primorial base Niven numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A328205, A328209, A328213, A330927, A330931, A333426.

max = 6; bases = Prime @ Range[max, 1, -1]; nmax = Times @@ bases - 1; primNivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n, MixedRadix[bases]]]; q1 = primNivenQ[1]; seq = {}; Do[q2 = primNivenQ[n]; If[q1 && q2, AppendTo[seq, n - 1]]; q1 = q2, {n, 2, nmax}]; seq

A331820 Positive numbers k such that k and k + 1 are both negabinary-Niven numbers (A331728).

Original entry on oeis.org

1, 2, 3, 8, 14, 15, 20, 32, 35, 56, 62, 63, 68, 80, 90, 95, 124, 125, 128, 174, 184, 185, 215, 224, 244, 245, 248, 254, 255, 260, 272, 275, 300, 304, 305, 320, 335, 342, 468, 469, 484, 485, 512, 515, 544, 545, 552, 575, 594, 636, 720, 762, 784, 785, 804, 846, 896

Offset: 1

Amiram Eldar, Jan 27 2020

			8 is a term since both 8 and 8 + 1 = 9 are negabinary-Niven numbers: A039724(8) = 11000 and 1 + 1 + 0 + 0 + 0 = 2 is a divisor of 8, and A039724(9) = 11001 and 1 + 1 + 0 + 0 + 1 = 3 is a divisor of 9.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A027615, A039724, A328209, A328213, A330927, A330931, A331086, A331089, A331728.

negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[n]]; c = 0; k = 1; s = {}; v = Table[-1, {2}]; While[c < 60, If[negaBinNivenQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 1]]]; k++]; s

A334309 Numbers k such that k and k+1 are both base phi Niven numbers (A334308).

Original entry on oeis.org

1, 15, 35, 90, 95, 231, 644, 728, 944, 1016, 1110, 1331, 1629, 1736, 1770, 1899, 1925, 2232, 2255, 2384, 2456, 2629, 2652, 2760, 3104, 3176, 3288, 3444, 3729, 3789, 3860, 4410, 4415, 4509, 4544, 4718, 4939, 4960, 5229, 5239, 5489, 5789, 5831, 5984, 6039, 6111

Offset: 1

Amiram Eldar, Apr 22 2020

			1 is a term since 1 and 2 are both base phi Niven numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A328205, A328209, A328213, A330927, A330931, A333427, A334308.

phiDigSum[1] = 1; phiDigSum[n_] := Plus @@ RealDigits[n, GoldenRatio, 2*Ceiling[ Log[GoldenRatio, n] ]][[1]]; phiNivenQ[n_] := Divisible[n, phiDigSum[n]]; Select[Range[6000], phiNivenQ[#] && phiNivenQ[# + 1] &]

A342427 Numbers k such that k and k + 1 are both Niven numbers in base 3/2 (A342426).

Original entry on oeis.org

1, 168, 459, 1817, 2196, 2197, 2655, 3128, 3280, 3699, 4199, 4575, 4927, 5184, 5795, 6600, 7215, 7259, 7656, 7657, 8448, 9636, 11304, 11339, 12492, 14160, 14175, 14424, 14805, 15624, 15625, 16335, 16336, 16925, 17802, 19170, 20349, 20811, 21624, 21735, 22197

Offset: 1

Amiram Eldar, Mar 11 2021

			168 is a term since both 168 and 169 are Niven numbers in base 3/2. 168 in base 3/2 is 2120220210 and 2+1+2+0+2+2+0+2+1+0 = 12 is a divisor of 168. 169 in base 3/2 is 2120220211 and 2+1+2+0+2+2+0+2+1+1 = 13 is a divisor of 169.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Subsequence of A342426.
Subsequences: A342428 and A342429.
Similar sequences: A330927 (decimal), A328205 (factorial), A328209 (Zeckendorf), A328213 (lazy Fibonacci), A330931 (binary), A331086 (negaFibonacci), A333427 (primorial), A334309 (base phi), A331820 (negabinary).

s[0] = 0; s[n_] := s[n] = s[2*Floor[n/3]] + Mod[n, 3]; q[n_] := Divisible[n, s[n]]; Select[Range[22000], q[#] && q[# + 1] &]

A344342 Numbers k such that k and k + 1 are both Gray-code Niven numbers (A344341).

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 14, 15, 27, 30, 31, 32, 39, 44, 51, 56, 62, 63, 75, 99, 104, 111, 123, 126, 127, 128, 135, 144, 155, 159, 174, 175, 184, 185, 195, 204, 207, 215, 224, 231, 234, 235, 243, 244, 248, 254, 255, 264, 275, 284, 294, 300, 304, 305, 315, 335, 354, 375

Offset: 1

Amiram Eldar, May 15 2021

			1 is a term since 1 and 2 are both Gray-code Niven numbers.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A005811, A014550.
Subsequence of: A344341.
Subsequences: A344343 and A344344.
Similar sequences: A330927 (decimal), A328205 (factorial), A328209 (Zeckendorf), A328213 (lazy Fibonacci), A330931 (binary), A331086 (negaFibonacci), A333427 (primorial), A334309 (base phi), A331820 (negabinary), A342427 (base 3/2).

gcNivenQ[n_] := Divisible[n, DigitCount[BitXor[n, Floor[n/2]], 2, 1]]; Select[Range[400], And @@ gcNivenQ[# + {0, 1}] &]

cp's OEIS Frontend

A005349 Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.

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A154701 Numbers k such that k, k + 1 and k + 2 are 3 consecutive Harshad numbers.

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A330931 Numbers k such that both k and k + 1 are Niven numbers in base 2 (A049445).

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A141769 Beginning of a run of 4 consecutive Niven (or Harshad) numbers.

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A331086 Positive numbers k such that k and k + 1 are both negaFibonacci-Niven numbers (A331085).

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A333427 Numbers k such that k and k+1 are both primorial base Niven numbers (A333426).

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