cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A245065 Second smallest multiple of n whose digits sum to n.

Original entry on oeis.org

10, 20, 12, 40, 50, 24, 70, 80, 18, 280, 308, 84, 364, 392, 285, 592, 629, 288, 1387, 4880, 588, 2596, 1886, 1896, 5875, 5876, 1998, 8596, 7598, 48990, 9796, 27968, 43989, 37978, 59885, 38988, 38998, 76988, 67899, 789880, 188969, 189798, 179998, 489896, 589995
Offset: 1

Views

Author

L. Edson Jeffery, Jul 11 2014

Keywords

Comments

Smallest multiple of n whose digits sum to n is A002998(n).

Links

Crossrefs

Second column of A245062.
Cf. A002998, A005349.

A077754 Smallest multiple of n with two or more digits, none of them zeros, whose digit sum equals n, or 0 if no such multiple exists.

Original entry on oeis.org

0, 0, 12, 112, 0, 24, 133, 152, 18, 0, 0, 48, 247, 266, 195, 448, 476, 198, 874, 0, 399, 2398, 1679, 888, 4975, 1898, 999, 7588, 4988, 0, 8959, 17888, 42999, 28798, 57995, 29988, 37999, 59888, 49998, 0, 177899, 88998, 99889, 479996, 499995, 589996
Offset: 1

Views

Author

Amarnath Murthy, Nov 20 2002

Keywords

Comments

Equivalently, the digits of a(n) are a nontrivial composition of n and n divides a(n).
Conjecture: zero occurs only for indices which are multiples of 10 apart from 1, 2, 5 and 11. (a(n) = 0 only for n = 1,2,5,11 or n = 10k.)

Examples

			a(8) = 152 is a multiple of 8; a(10) = 0, since every multiple of 10 includes a 0.

Links

Crossrefs

Cf. A002998, A069035.

Extensions

Edited and extended by Franklin T. Adams-Watters, Jun 14 2006
a(44) corrected by Chai Wah Wu, Mar 17 2016

A191872 a(n) is the smallest multiple of n such that the sum of the square of the decimal digits of a(n) is divisible by n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 130, 1265, 60, 143, 154, 360, 48, 1071, 396, 133, 240, 693, 1386, 1817, 888, 50, 286, 999, 2408, 2552, 390, 372, 448, 1419, 2992, 315, 2268, 1295, 266, 3666, 480, 1148, 1344, 129, 11176, 360, 3818, 329, 8880, 2254, 550, 1071, 2444, 2597, 2268, 12485, 2688, 399, 2552, 12449, 111960, 549, 372, 693, 8000
Offset: 1

Views

Author

Michel Lagneau, Jun 18 2011

Keywords

Examples

			a(11) =1265 because 11*115 = 1265 and 1^2+2^2+6^2+5^2 = 66 = 11*6.

Links

Crossrefs

Cf. A002998, A131382.

Programs

  • Maple
    with(numtheory):for n from 1 to 80 do:id:=0:for k from 1 to 1000000 while(id=0)
  do :l:=length(k):n0:=k:s1:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q,
  10):n0:=v :s1:=s1+u^2 :od: :if irem(k,n) =0 and irem(s1,n)=0 then id:=1:printf(`%d,
  `, k):else fi:od: od:
  • Mathematica
    smn[n_]:=Module[{k=1},While[Mod[Total[IntegerDigits[k n]^2],n]!=0,k++];n k]; Array[smn,70] (* Harvey P. Dale, Feb 13 2023 *)
  • PARI
    a(n)=my(s);forstep(k=n,9e9,n,s=eval(Vec(Str(k)));if(sum(i=1,#s,s[i]^2)%n==0,return(k))) \\ Charles R Greathouse IV, Jun 20 2011

A334403 Harshad numbers with sum of digits equal to 18.

Original entry on oeis.org

198, 288, 378, 396, 468, 486, 558, 576, 594, 648, 666, 684, 738, 756, 774, 792, 828, 846, 864, 882, 918, 936, 954, 972, 990, 1098, 1188, 1278, 1296, 1368, 1386, 1458, 1476, 1494, 1548, 1566, 1584, 1638, 1656, 1674, 1692, 1728, 1746, 1764, 1782, 1818, 1836, 1854
Offset: 1

Views

Author

Davide Rotondo, Sep 08 2020

Keywords

Comments

Even numbers with sum of digits equal to 18 are Harshad numbers (A005349).
If k is a term, then so is 10*k. - Robert Israel, Mar 26 2023

Examples

			198/18 = 11.

Links

Crossrefs

Intersection of A005349 and A235228.
Subsequence of A008600.
Cf. A002998.

Programs

  • Maple
    filter:= n -> convert(convert(n,base,10),`+`) = 18:
select(filter, [seq(i,i=18...4000, 18)]); # Robert Israel, Mar 26 2023
  • Mathematica
    Select[18 * Range[100], Plus @@ IntegerDigits[#] == 18 &] (* Amiram Eldar, Sep 08 2020 *)
  • PARI
    isok(m) = my(s=sumdigits(m)); (s==18) && !(m%s); \\ Michel Marcus, Sep 08 2020
  • PARI
    first(n) = {my(res = vector(n), t = 0); forstep(i = 18, oo, 18, if(vecsum(digits(i)) == 18, t++; res[t] = i; if(t >= n, return(res) ) ) ) } \\ David A. Corneth, Sep 08 2020

Extensions

More terms from Michel Marcus, Sep 08 2020

A256886 Smallest multiple of prime(n) whose digits sum is divisible by prime(n).

Original entry on oeis.org

2, 3, 5, 7, 209, 247, 476, 874, 1679, 4988, 8959, 37999, 177899, 99889, 686999, 2989889, 8888999, 9998998, 58999999, 289999997, 499988899, 999899998, 5989989899, 9989999999, 99999999898, 2918999999999, 699999899899, 1999989999989, 4889999999989, 8899999999898
Offset: 1

Views

Author

Michel Lagneau, Apr 12 2015

Keywords

Comments

Subsequence of A002998.

Examples

			a(5)=209 is in the sequence because prime(5)=11 divides 2+0+9 and 209.

Crossrefs

Cf. A000040, A002998.

Programs

  • Mathematica
    Flatten[Table[Select[Prime[n] Range[10^8],Total[IntegerDigits[#]]==Prime[n]&,1],{n,1,21}]]
  • PARI
    lista(nn) = {forprime(p=2, nn, k = 1; while(((q = k*p) && (sumdigits(q) % p)), k++); print1(q, ", "););} \\ Michel Marcus, Apr 14 2015

Formula

a(n) = A002998(A000040(n)).
Previous Showing 11-15 of 15 results.

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