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.

Showing 1-4 of 4 results.

A088398 a(n) = A069528(n)/n.

Original entry on oeis.org

9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 0, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 0, 9, 3, 9, 9, 1, 9, 9, 3, 36, 36, 0, 9, 9, 1, 9, 9, 3, 9, 27, 3, 27, 0, 1, 9, 9, 3, 9, 9, 3, 27, 27, 1, 0, 9, 3, 9, 9, 3, 171, 18, 1, 18, 18, 0, 9, 9, 3, 9, 72, 1, 18, 18, 3, 27, 0, 3, 9, 9, 1, 27, 27, 3, 18, 27, 3, 0, 9, 1, 144, 36, 12, 45
Offset: 1

Views

Author

Ray Chandler, Sep 28 2003

Keywords

Crossrefs

Cf. A069528.

A069530 Smallest multiple of n with digit sum = 11, or 0 if no such number exists.

Original entry on oeis.org

29, 38, 0, 56, 65, 0, 56, 56, 0, 290, 209, 0, 65, 56, 0, 128, 119, 0, 38, 380, 0, 308, 92, 0, 425, 182, 0, 56, 29, 0, 155, 128, 0, 272, 245, 0, 74, 38, 0, 560, 164, 0, 344, 308, 0, 92, 47, 0, 245, 650, 0, 416, 371, 0, 605, 56, 0, 290, 236, 0, 1037, 434, 0, 128, 65, 0, 335
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Comments

a(n) = 0 if n is divisible by 3, 1111, 1507, 2849, 3367, 4849, 5291 or 7373. - Robert Israel, Feb 14 2024

Crossrefs

Programs

  • Maple
    A069530 := proc(n)
        local m ;
        if modp(n,3) = 0 then
             0 ;
        else
            for m from 1 do
                if digsum(m*n) = 11 then
                    return m*n ;
                end if;
            end do:
        end if;
    end proc:
    seq(A069530(n),n=1..70) ; # R. J. Mathar, Aug 06 2019
  • PARI
    sod(n) = {digs = digits(n); return (sum(i=1, #digs, digs[i]));}
    a(n) = {if (n % 3 == 0, return (0)); k = 1; while (sod(k*n) != 11, k++); k;} \\ Michel Marcus, Sep 14 2013

Formula

a(3k) = 0 for k = 1, 2, 3, ....
a(n) = n*A088400(n). - R. J. Mathar, Aug 06 2019

Extensions

More terms from Sascha Kurz, Apr 08 2002

A069526 Smallest multiple of n with digit sum = 7, or 0 if no such number exists, e.g. a(3k)= a(11k) = 0.

Original entry on oeis.org

7, 16, 0, 16, 25, 0, 7, 16, 0, 70, 0, 0, 52, 70, 0, 16, 34, 0, 133, 160, 0, 0, 115, 0, 25, 52, 0, 700, 232, 0, 124, 160, 0, 34, 70, 0, 0, 304, 0, 160, 205, 0, 43, 0, 0, 322, 1222, 0, 2401, 250, 0, 52, 106, 0, 0, 7000, 0, 232, 4012, 0, 61, 124, 0, 1024, 520, 0, 11122, 340
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Comments

Either no multiples of 37 have digit sum 7 or their first values are > 10000000. - Larry Reeves (larryr(AT)acm.org), Jul 02 2002
No multiples of 3, 11, 37, 101 or 271 have digit sum 7. - Robert Israel, Feb 13 2024

Crossrefs

Programs

  • Maple
    unfinished:= true: V:= Vector(300): V0:= select(t -> igcd(t, 3*11*37*101*271) = 1, {$1..300}):
    for i1 from 0 while unfinished do
      for i2 from 0 to i1 while unfinished do
        for i3 from 0 to i2 while unfinished do
          for i4 from 0 to i3 while unfinished do
            for i5 from 0 to i4 while unfinished do
              for i6 from 0 to i5 while unfinished do
                for i7 from 0 to i6 while unfinished do
                  v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7;
                  dv:= numtheory:-divisors(v);
                  for s in V0 intersect dv do
                    V[s]:= v;
                  od;
                  V0:= V0 minus dv;
                  unfinished:= evalb(V0 <> {});
    od od od od od od od:
    convert(V,list); # Robert Israel, Feb 13 2024

Formula

a(n)= n*A088396(n). - R. J. Mathar, Aug 06 2019

Extensions

More terms from Larry Reeves, Jul 02 2002

A069529 Smallest multiple of n with digit sum = 10, or 0 if no such number exists, e.g. a(3k)= 0.

Original entry on oeis.org

19, 28, 0, 28, 55, 0, 28, 64, 0, 190, 55, 0, 91, 28, 0, 64, 136, 0, 19, 280, 0, 154, 46, 0, 325, 208, 0, 28, 145, 0, 217, 64, 0, 136, 280, 0, 37, 190, 0, 280, 82, 0, 172, 352, 0, 46, 235, 0, 343, 550, 0, 208, 424, 0, 55, 280, 0, 406, 118, 0, 244, 1054, 0, 64, 325, 0, 1072
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Comments

a(n) = 0 if n is a multiple of 3, 1111, 2849, 3367, 4649 or 5291.

Crossrefs

Programs

  • Maple
    unfinished:= true: V:= Vector(1000):
    V0:= select(t -> igcd(t, 3*4649) = 1 and t mod 1111 <> 0 and t mod 2849 <> 0 and t mod 3367 <> 0 and t mod 5291 <> 0, {$1..1000}):
    for i1 from 0 while unfinished do
      for i2 from 0 to i1 while unfinished do
        for i3 from 0 to i2 while unfinished do
          for i4 from 0 to i3 while unfinished do
            for i5 from 0 to i4 while unfinished do
              for i6 from 0 to i5 while unfinished do
                for i7 from 0 to i6 while unfinished do
                for i8 from 0 to i7 while unfinished do
                for i9 from 0 to i8 while unfinished do
                for i10 from 0 to i9 while unfinished do
                  v:= 10^i1 + 10^i2 + 10^i3 + 10^i4 + 10^i5 + 10^i6 + 10^i7 + 10^i8 + 10^i9 + 10^i10;
                  if convert(convert(v,base,10),`+`) <> 10 then next fi;
                  dv:= numtheory:-divisors(v);
                  for s in V0 intersect dv do
                    V[s]:= v;
                  od;
                  V0:= V0 minus dv;
                  unfinished:= evalb(V0 <> {});
    od od od od od od od od od od:
    convert(V,list); # Robert Israel, Feb 14 2024

Extensions

More terms from Sascha Kurz, Apr 08 2002
Showing 1-4 of 4 results.