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 1-7 of 7 results.

A063997 Multiples of 4 whose digits add to 4.

Original entry on oeis.org

4, 40, 112, 220, 400, 1012, 1120, 1300, 2020, 2200, 3100, 4000, 10012, 10120, 10300, 11020, 11200, 12100, 13000, 20020, 20200, 21100, 22000, 30100, 31000, 40000, 100012, 100120, 100300, 101020, 101200, 102100, 103000, 110020, 110200, 111100
Offset: 1

Views

Author

Lisa O. Coulter (lcoulter(AT)stetson.edu), Sep 06 2001

Keywords

Examples

			4 is an element of the sequence, since 4 is a multiple of 4 the sum of whose digits is 4; 220 is an element of the sequence, since 220 = 4*55 and 2 + 2+ 0 = 4.

Links

Crossrefs

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217.
Row n=4 of A245062.

Programs

  • Mathematica
    Select[4Range[120000],Total[IntegerDigits[#]]==4&] (* Harvey P. Dale, May 07 2011 *)
  • PARI
    SumDE(x,y)= { local(s); s=0; while (x>9 && sHarry J. Smith, Sep 05 2009

Extensions

More terms from Ray Chandler, Sep 28 2003

A062768 Multiples of 6 such that the sum of the digits is equal to 6.

Original entry on oeis.org

6, 24, 42, 60, 114, 132, 150, 204, 222, 240, 312, 330, 402, 420, 510, 600, 1014, 1032, 1050, 1104, 1122, 1140, 1212, 1230, 1302, 1320, 1410, 1500, 2004, 2022, 2040, 2112, 2130, 2202, 2220, 2310, 2400, 3012, 3030, 3102, 3120, 3210, 3300, 4002, 4020, 4110
Offset: 1

Views

Author

Lisa O Coulter (lisa_coulter(AT)my-deja.com), Jul 17 2001

Keywords

Comments

Even numbers with sum of digits equal to 6 are Harshad numbers (A005349). - Davide Rotondo, Sep 04 2020

Examples

			60 is a member of the sequence since 60 / 6 = 10 and 6 + 0 = 6; 114 is also an element since 114 is divisible by 6 and 1 + 1+ 4 = 6.

Links

Crossrefs

Cf. A063416, A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540.
Subsequence of A005349.
Row n=6 of A245062.

Programs

  • ARIBAS
    : var stk: stack; end; minarg := 0; maxarg := 900; n := 6; for k := minarg to maxarg do m := k*n; s := itoa(m); for j := 0 to length(s) - 1 do stack_push(stk,atoi(s[j..j])); end; if sum(stack2array(stk)) = n then write(m," "); end; end;.
  • Mathematica
    Select[ Range[ 6, 4200, 6 ], Plus @@ IntegerDigits[ # ] == 6 & ]

Extensions

More terms from Klaus Brockhaus, Jul 20 2001

A063416 Multiples of 7 whose sum of digits is equal to 7.

Original entry on oeis.org

7, 70, 133, 322, 511, 700, 1015, 1141, 1204, 1330, 2023, 2212, 2401, 3031, 3220, 4102, 5110, 7000, 10024, 10150, 10213, 10402, 11032, 11221, 11410, 12040, 12103, 13111, 13300, 15001, 20041, 20104, 20230, 21112, 21301, 22120, 23002, 24010
Offset: 1

Views

Author

Klaus Brockhaus, Jul 20 2001

Keywords

Comments

Numbers are all 7 mod 63.

Examples

			133 = 19*7 and 1+3+3 = 7, so 133 is a term of this sequence.

Links

Crossrefs

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540, A062768.
Row n=7 of A245062.

Programs

  • ARIBAS
    : var stk: stack; end; minarg := 0; maxarg := 5000; n := 7; for k := minarg to maxarg do m := k*n; s := itoa(m); for j := 0 to length(s) - 1 do stack_push(stk,atoi(s[j..j])); end; if sum(stack2array(stk)) = n then write(m," "); end; end;.
  • Mathematica
    Select[Range[7, 25000, 7], Plus @@ IntegerDigits[ # ] == 7 &]
  • PARI
    forstep(m=0, 70000, 7, if(vecsum(digits(m))==7, print1(m, ", "))) \\ Harry J. Smith, Aug 20 2009

A069540 Multiples of 5 with digit sum 5.

Original entry on oeis.org

5, 50, 140, 230, 320, 410, 500, 1040, 1130, 1220, 1310, 1400, 2030, 2120, 2210, 2300, 3020, 3110, 3200, 4010, 4100, 5000, 10040, 10130, 10220, 10310, 10400, 11030, 11120, 11210, 11300, 12020, 12110, 12200, 13010, 13100, 14000, 20030, 20120
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Links

Crossrefs

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997.
Row n=5 of A245062.

Programs

  • Mathematica
    Select[5*Range[5000],Total[IntegerDigits[#]]==5&] (* Harvey P. Dale, Nov 08 2017 *)

Extensions

Corrected and extended by Ray Chandler, Sep 28 2003

A069534 Smallest multiple of 5 with digit sum n.

Original entry on oeis.org

10, 20, 30, 40, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 195, 295, 395, 495, 595, 695, 795, 895, 995, 1995, 2995, 3995, 4995, 5995, 6995, 7995, 8995, 9995, 19995, 29995, 39995, 49995, 59995, 69995, 79995, 89995, 99995, 199995, 299995, 399995, 499995, 599995
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Comments

a(6) onwards the pattern is evident.

Links

Crossrefs

Cf. A069521 to A069530, A069532, A069533.
Cf. A077492.

Programs

  • Mathematica
    t={}; Do[i=5; While[Total[IntegerDigits[i]]!=n,i=i+5]; AppendTo[t,i],{n,46}]; t (* Jayanta Basu, May 19 2013 *)
With[{f=5*Range[200000]},Flatten[Table[Select[f,Total[IntegerDigits[#]] == n&,1],{n,50}]]] (* Harvey P. Dale, Dec 31 2013 *)
  • PARI
    A069534(n)=(((n+4)%9+1)*10^((n+4)\9)-5)*10^(n<5) \\ M. F. Hasler, Sep 16 2016

Formula

a(n) = ((n+4)%9+1)*10^floor((n+4)/9)-5 for all n > 4, where % is the binary mod/remainder operator. - M. F. Hasler, Sep 16 2016
From Chai Wah Wu, Sep 15 2020: (Start)
a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 14.
G.f.: 5*x*(72*x^13 - 18*x^12 - 18*x^11 - 18*x^10 - 18*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^5 - 7*x^4 + 2*x^3 + 2*x^2 + 2*x + 2)/((x - 1)*(10*x^9 - 1)). (End)
a(n) = 5 * A077492(n). - Alois P. Heinz, Sep 15 2020

Extensions

More terms from Ray Chandler, Jul 28 2003

A069543 Multiples of 8 with digit sum 8.

Original entry on oeis.org

8, 80, 152, 224, 440, 512, 800, 1016, 1160, 1232, 1304, 1520, 2024, 2240, 2312, 2600, 3032, 3104, 3320, 4040, 4112, 4400, 5120, 6200, 8000, 10016, 10160, 10232, 10304, 10520, 11024, 11240, 11312, 11600, 12032, 12104, 12320, 13040, 13112, 13400
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Links

Crossrefs

Cf. A069521 to A069530, A069532, A069533, A069534, A069535, A069536, A069537, A052217, A063997, A069540, A062768, A063416.
Row n=8 of A245062.

Extensions

More terms from Ray Chandler, Sep 28 2003

A069536 Smallest multiple of 8 with digit sum n.

Original entry on oeis.org

0, 1000, 200, 120, 40, 32, 24, 16, 8, 72, 64, 56, 48, 184, 176, 96, 88, 296, 288, 496, 488, 696, 688, 896, 888, 1888, 2888, 3888, 4888, 5888, 6888, 7888, 8888, 9888, 19888, 29888, 39888, 49888, 59888, 69888, 79888, 89888, 99888
Offset: 0

Views

Author

Amarnath Murthy, Apr 01 2002

Keywords

Comments

a(25) onwards the pattern is evident.

Crossrefs

Cf. A069521 to A069530, A069532, A069533, A069534, A069535.

Programs

  • Haskell
    a069536 n = a069536_list !! n
a069536_list = map (* 8) a077495_list
-- Reinhard Zumkeller, Dec 09 2011

Formula

a(n) = 8 * A077495(n).

Extensions

Missing a(0) inserted by Franklin T. Adams-Watters, Nov 29 2011
Showing 1-7 of 7 results.

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