A061383 -id:A061383 - cp's OEIS frontend

A062185 Harmonic mean of digits is 8.

8, 88, 888, 6999, 8888, 9699, 9969, 9996, 68999, 69899, 69989, 69998, 86999, 88888, 89699, 89969, 89996, 96899, 96989, 96998, 98699, 98969, 98996, 99689, 99698, 99869, 99896, 99968, 99986, 688999, 689899, 689989, 689998, 698899, 698989

Offset: 1

Vladeta Jovovic, Jun 12 2001

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 8, Print[n]], {n, 1, 10^6}]
Select[Range[700000],DigitCount[#,10,0]==0&&HarmonicMean[IntegerDigits[ #]]==8&] (* Harvey P. Dale, Jan 27 2012 *)

More terms from Robert G. Wilson v, Aug 08 2001

A061385 Numbers n such that sum of digits = twice number of digits.

Original entry on oeis.org

2, 13, 22, 31, 40, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600, 1007, 1016, 1025, 1034, 1043, 1052, 1061, 1070, 1106, 1115, 1124, 1133, 1142, 1151, 1160, 1205, 1214, 1223, 1232, 1241, 1250, 1304

Offset: 1

Amarnath Murthy, May 03 2001

			141 is a term as the arithmetic mean of the digits is (1+4+1)/3 = 2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A061383, A061384, A061386, A061387, A061388, A061423, A061424, A061425.

[ n: n in [1..1310] | &+Intseq(n) eq 2*#Intseq(n) ];  // Bruno Berselli, Jun 30 2011

S:= proc(d,k,flag) option remember;
  if d = 1 then
    if k >= 0 and k <= 9 then return [k]
    else return []
    fi
  fi;
  [seq(op(map(`+`, procname(d-1,k-i,0), i*10^(d-1))),i=flag..min(k,9))]
end proc:
seq(op(S(d,2*d,1)),d=1..5); # Robert Israel, Apr 23 2017

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

A061387 Sum of digits = 4 times number of digits.

Original entry on oeis.org

4, 17, 26, 35, 44, 53, 62, 71, 80, 129, 138, 147, 156, 165, 174, 183, 192, 219, 228, 237, 246, 255, 264, 273, 282, 291, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 408, 417, 426, 435, 444, 453, 462, 471, 480, 507, 516, 525, 534, 543, 552, 561, 570, 606

Offset: 1

Amarnath Murthy, May 03 2001

			147 is a term as the arithmetic mean of the digits is (1+4+7)/3 = 4.

Cf. A061383, A061384, A061385, A061386, A061388, A061423, A061424, A061425.

[ n: n in [1..610] | &+Intseq(n) eq 4*#Intseq(n) ];  // Bruno Berselli, Jun 30 2011

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

A180160 (sum of digits) mod (number of digits) of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2

Offset: 0

Reinhard Zumkeller, Aug 15 2010

a(n) = A007953(n) mod A055642(n);
a(A061383(n)) = 0; a(A180157(n)) > 0;
a(repdigits)=0: a(A010785(n))=0: a(A002275(n))=0: a(A002276(n))=0: a(A002277(n))=0: a(A002278(n))=0: a(4(n))=0: a(A002279(n))=0: a(A002280(n))=0: a(A002281(n))=0: a(A002282(n))=0: a(A002283(n))=0;
A123522 gives smallest m such that a(m) = n.

Reinhard Zumkeller, Table of n, a(n) for n = 0..25000

Cf. A002275-A002283, A007953, A010785, A055642, A061383, A123522, A180157, A374097.

A180160[n_] := If[n == 0, 0, Mod[Total[#], Length[#]] & [IntegerDigits[n]]];
Array[A180160, 100, 0] (* Paolo Xausa, Jun 30 2024 *)
Join[{0},Table[Mod[Total[IntegerDigits[n]],IntegerLength[n]],{n,110}]] (* Harvey P. Dale, Jul 30 2025 *)

A371383 a(n) is the numerator of the arithmetic mean of the digits of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 4, 9, 5, 11, 6

Offset: 0

Stefano Spezia, Mar 20 2024

Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for Colombian or self numbers and related sequences.

Cf. A004426, A004427, A007953, A055642, A061383, A371384 (denominator).

a[n_]:=Numerator[Mean[IntegerDigits[n]]]; Array[a,85,0]

from math import gcd
def A371383(n): return (l:=sum(map(int,(s:=str(n)))))//gcd(l,len(s)) # Chai Wah Wu, Mar 22 2024

A371384 a(n) is the denominator of the arithmetic mean of the digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2

Offset: 0

Stefano Spezia, Mar 20 2024

Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for Colombian or self numbers and related sequences.

Cf. A004426, A004427, A007953, A055642, A061383, A371383 (numerator).

a[n_]:=Denominator[Mean[IntegerDigits[n]]]; Array[a,90,0]

from math import gcd
def A371384(n): return (l:=len(s:=str(n)))//gcd(l,sum(map(int,s))) # Chai Wah Wu, Mar 22 2024

A061386 Sum of digits = 3 times number of digits.

Original entry on oeis.org

3, 15, 24, 33, 42, 51, 60, 108, 117, 126, 135, 144, 153, 162, 171, 180, 207, 216, 225, 234, 243, 252, 261, 270, 306, 315, 324, 333, 342, 351, 360, 405, 414, 423, 432, 441, 450, 504, 513, 522, 531, 540, 603, 612, 621, 630, 702, 711, 720, 801, 810, 900, 1029

Offset: 1

Amarnath Murthy, May 03 2001

			126 is a term as the arithmetic mean of the digits is (1+2+6)/3 = 3.

Cf. A061383-A061388, A061423-A061425.

[ n: n in [1..1030] | &+Intseq(n) eq 3*#Intseq(n) ];  // Bruno Berselli, Jun 30 2011

Select[Range[1200],3IntegerLength[#]==Total[IntegerDigits[#]]&]  (* Harvey P. Dale, Feb 04 2011 *)

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 102, 111, 120, 123, 132, 135, 147, 153, 159, 174, 195, 201, 204, 210, 213, 222, 231, 234, 240, 243, 246, 258, 264, 285, 306, 312, 315, 321, 324, 333, 342, 345, 351, 354, 357, 360, 369, 375, 396, 402

Offset: 1

Claudio Meller, Aug 09 2010

Subsequence of A061383.

A180160(a(n)) = 0. - Reinhard Zumkeller, Aug 15 2010

			135 is in the list because (1+3+5)/3 = 3 and 3 is a digit of 135.

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953, A055642, A004426, A004427; A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539.

Cf. A052018. - Reinhard Zumkeller, Aug 15 2010

a175688 n = a175688_list !! (n-1)
a175688_list = filter f [0..] where
   f x = m == 0 && ("0123456789" !! avg) `elem` show x
         where (avg, m) = divMod (a007953 x) (a055642 x)
-- Reinhard Zumkeller, Jun 18 2013

idQ[n_]:=Module[{idn=IntegerDigits[n],m},m=Mean[idn];IntegerQ[m] && MemberQ[idn,m]]; Select[Range[0,500],idQ] (* Harvey P. Dale, Jun 10 2011 *)

Edited by Reinhard Zumkeller, Aug 13 2010

A180157 Arithmetic mean of digits is not an integer.

Original entry on oeis.org

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 104, 106, 107, 109, 110, 112, 113, 115, 116, 118, 119, 121, 122, 124, 125

Offset: 1

Reinhard Zumkeller, Aug 15 2010

Complement of A061383; A180160(a(n)) > 0;
A004426(a(n)) <> A004427(a(n)).
It seems 'obvious' that a(n) ~ n; is this true? - Charles R Greathouse IV, Feb 06 2013

R. Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A007953, A055642.

Select[Range[200],!IntegerQ[Mean[IntegerDigits[#]]]&]  (* Harvey P. Dale, Mar 27 2011 *)

is(n)=my(v=digits(n));sum(i=1,#v,v[i])%#v>0 \\ Charles R Greathouse IV, Feb 06 2013

A062180 Harmonic mean of digits is 2.

Original entry on oeis.org

2, 22, 136, 144, 163, 222, 316, 361, 414, 441, 613, 631, 1236, 1244, 1263, 1326, 1333, 1362, 1424, 1442, 1623, 1632, 2136, 2144, 2163, 2222, 2316, 2361, 2414, 2441, 2613, 2631, 3126, 3133, 3162, 3216, 3261, 3313, 3331, 3612, 3621, 4124, 4142, 4214, 4241

Offset: 1

Vladeta Jovovic, Jun 12 2001

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A062179-A062185, A061383-A061388, A061423-A061425.

h:= proc(L) local m,x,i,t;
  m:= nops(L)+1;
  x:= m/2 - add(1/t, t=L);
  if x > 0 then
    x:= 1/x;
    if x::posint and x <= 9 then
      return(x + add(L[i]*10^i,i=1..m-1))
  fi fi
end proc:
f:= n -> h(map(`+`,convert(n,base,9),1)):
g:= n -> h([op(map(`+`,convert(n,base,9),1)),1]):
R:= 2:
for d from 1 to 4 do
  R:= R, seq(f(i),i=9^(d-1)..9^d-1),seq(g(i),i=9^(d-1)..9^d-1)
od:
R; # Robert Israel, Apr 05 2021

Do[ h = IntegerDigits[n]; If[ Sort[h][[1]] != 0 && Length[h]/Apply[Plus, 1/h] == 2, Print[n]], {n, 1, 10^4}]

More terms from Henry Bottomley, Jul 25 2001

cp's OEIS Frontend

A062185 Harmonic mean of digits is 8.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions

A061385 Numbers n such that sum of digits = twice number of digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Extensions

A061387 Sum of digits = 4 times number of digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Extensions

A180160 (sum of digits) mod (number of digits) of n in decimal representation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A371383 a(n) is the numerator of the arithmetic mean of the digits of n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

A371384 a(n) is the denominator of the arithmetic mean of the digits of n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

A061386 Sum of digits = 3 times number of digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

Extensions

A175688 Numbers k with property that arithmetic mean of its digits is both an integer and one of the digits of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions

A180157 Arithmetic mean of digits is not an integer.

Views