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.

Previous Showing 11-19 of 19 results.

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

A077495 a(n) = smallest k such that the digit sum of 8k is n.

Original entry on oeis.org

0, 125, 25, 15, 5, 4, 3, 2, 1, 9, 8, 7, 6, 23, 22, 12, 11, 37, 36, 62, 61, 87, 86, 112, 111, 236, 361, 486, 611, 736, 861, 986, 1111, 1236, 2486, 3736, 4986, 6236, 7486, 8736, 9986, 11236, 12486, 24986, 37486, 49986, 62486, 74986, 87486, 99986, 112486, 124986
Offset: 0

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Crossrefs

A069536(n)/8.
Cf. A051885, A069532, A069534, A069536, A077493, A077494.

Programs

  • Haskell
    import Data.List (elemIndex)
import Data.Maybe (fromJust)
a077495 n = fromJust $ elemIndex n $ map a007953 a008590_list
a077495_list = map a077495 [0..]
-- Reinhard Zumkeller, Dec 09 2011

Formula

From Robert Israel, Nov 19 2022: (Start) G.f.: -x^24*(985*x^9 - 125*x^8 - 125*x^7 - 125*x^6 - 125*x^5 - 125*x^4 - 125*x^3 - 125*x^2 - 125*x - 111)/((x - 1)*(10*x^9 - 1)) + 112*x^23 + 86*x^22 + 87*x^21 + 61*x^20 + 62*x^19 + 36*x^18 + 37*x^17 + 11*x^16 + 12*x^15 + 22*x^14 + 23*x^13 + 6*x^12 + 7*x^11 + 8*x^10 + 9*x^9 + x^8 + 2*x^7 + 3*x^6 + 4*x^5 + 5*x^4 + 15*x^3 + 25*x^2 + 125*x.
For n >= 24, a(n) = 125*A051885(n-24) + 111. (End)

Extensions

Corrected and extended by Ray Chandler, Aug 03 2003
Missing a(0)=0 added and offset adjusted by Reinhard Zumkeller, Dec 09 2011

A077491 a(n) = smallest k such that 2k has digit sum = n.

Original entry on oeis.org

5, 1, 6, 2, 7, 3, 8, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 99, 149, 199, 249, 299, 349, 399, 449, 499, 999, 1499, 1999, 2499, 2999, 3499, 3999, 4499, 4999, 9999, 14999, 19999, 24999, 29999, 34999, 39999, 44999, 49999, 99999, 149999, 199999, 249999, 299999
Offset: 1

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Links

Crossrefs

Cf. A069532, A069534.

Formula

a(n) = A069532(n)/2.

Extensions

More terms from Ray Chandler, Jul 28 2003

A077492 a(n) = smallest k such that 5k has a digit sum = n.

Original entry on oeis.org

2, 4, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 39, 59, 79, 99, 119, 139, 159, 179, 199, 399, 599, 799, 999, 1199, 1399, 1599, 1799, 1999, 3999, 5999, 7999, 9999, 11999, 13999, 15999, 17999, 19999, 39999, 59999, 79999, 99999, 119999, 139999, 159999, 179999
Offset: 1

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Links

Crossrefs

Cf. A069532, A069534.

Programs

  • Mathematica
    LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 10, -10},{2, 4, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}, 40] (* Georg Fischer, Oct 26 2020 *)

Formula

a(n) = A069534(n)/5.
a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 14. - Georg Fischer, Oct 26 2020

Extensions

More terms from Ray Chandler, Jul 28 2003

A077493 a(n) = smallest multiple of 7 with a digit sum = n.

Original entry on oeis.org

1001, 21, 112, 14, 42, 7, 35, 63, 28, 56, 84, 49, 77, 168, 196, 98, 189, 469, 497, 399, 679, 896, 798, 889, 1799, 2898, 2989, 3899, 4998, 6979, 5999, 8799, 9898, 9989, 29799, 19999, 39998, 58989, 59899, 68999, 79989, 99799, 89999, 199899, 389998
Offset: 2

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Crossrefs

Cf. A069532, A069534, A077494.

Extensions

Corrected and extended by Sascha Kurz, Jan 30 2003

A077494 a(n) = smallest k such that the digit sum of 7k is n.

Original entry on oeis.org

143, 3, 16, 2, 6, 1, 5, 9, 4, 8, 12, 7, 11, 24, 28, 14, 27, 67, 71, 57, 97, 128, 114, 127, 257, 414, 427, 557, 714, 997, 857, 1257, 1414, 1427, 4257, 2857, 5714, 8427, 8557, 9857, 11427, 14257, 12857, 28557, 55714, 42857, 71427, 85714, 99857, 112857, 128557
Offset: 2

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Crossrefs

Cf. A069532, A069534, A077493.

Programs

  • Mathematica
    sk7[n_]:=Module[{k=1},While[Total[IntegerDigits[7k]]!=n,k++];k]; Array[ sk7,60,2] (* Harvey P. Dale, Apr 07 2014 *)

Formula

A077493(n)/7

Extensions

Corrected and extended by Ray Chandler, Aug 03 2003

A077489 a(n) = smallest multiple of 4 with sum of digits = n.

Original entry on oeis.org

100, 20, 12, 4, 32, 24, 16, 8, 36, 28, 56, 48, 76, 68, 96, 88, 188, 288, 388, 488, 588, 688, 788, 888, 988, 1988, 2988, 3988, 4988, 5988, 6988, 7988, 8988, 9988, 19988, 29988, 39988, 49988, 59988, 69988, 79988, 89988, 99988, 199988, 299988, 399988, 499988
Offset: 1

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Crossrefs

Cf. A077490, A069532, A069534.

Programs

  • Mathematica
    With[{d4=Sort[{Total[IntegerDigits[#]],#}&/@(4Range[250000])]},Table[ SelectFirst[ d4,#[[1]]==n&],{n,50}]][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 17 2021 *)

Extensions

More terms from Ray Chandler, Aug 03 2003

A077490 a(n) = smallest k such that 4k has a digit sum = n.

Original entry on oeis.org

25, 5, 3, 1, 8, 6, 4, 2, 9, 7, 14, 12, 19, 17, 24, 22, 47, 72, 97, 122, 147, 172, 197, 222, 247, 497, 747, 997, 1247, 1497, 1747, 1997, 2247, 2497, 4997, 7497, 9997, 12497, 14997, 17497, 19997, 22497, 24997, 49997, 74997, 99997, 124997, 149997, 174997
Offset: 1

Views

Author

Amarnath Murthy, Nov 07 2002

Keywords

Crossrefs

Cf. A077489, A069532, A069534.

Formula

A077489(n)/4

Extensions

Corrected and extended by Sascha Kurz, Feb 10 2003

A205960 Smallest odd number with digit sum equal to n.

Original entry on oeis.org

1, 11, 3, 13, 5, 15, 7, 17, 9, 19, 29, 39, 49, 59, 69, 79, 89, 99, 199, 299, 399, 499, 599, 699, 799, 899, 999, 1999, 2999, 3999, 4999, 5999, 6999, 7999, 8999, 9999, 19999, 29999, 39999, 49999, 59999, 69999, 79999, 89999, 99999, 199999, 299999, 399999, 499999
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 02 2012

Keywords

Comments

Except for a(2), a(4), a(6) and a(8), the same as A051885 (n>0).

Links

Crossrefs

Cf. A051885, A069532.

Programs

  • Mathematica
    e = 5; Join[Table[l = 1; While[True, a = 2*l - 1; If[Total[IntegerDigits[a]] == n, Break[]]; l++]; a, {n, 8}], Flatten[Table[i*10^j - 1, {j, e}, {i, 9}]]]
With[{ds=Table[{n,Total[IntegerDigits[n]]},{n,1,600001,2}]},Table[ SelectFirst[ ds,#[[2]]==k&],{k,50}]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 30 2018 *)

Formula

a(n+1) = A069532(n) + 1.
From Chai Wah Wu, Sep 15 2020: (Start)
a(n) = a(n-1) + 10*a(n-9) - 10*a(n-10) for n > 18.
G.f.: x*(90*x^17 - 90*x^16 + 90*x^15 - 90*x^14 + 90*x^13 - 90*x^12 + 90*x^11 - 90*x^10 - 8*x^8 + 10*x^7 - 8*x^6 + 10*x^5 - 8*x^4 + 10*x^3 - 8*x^2 + 10*x + 1)/((x - 1)*(10*x^9 - 1)). (End)
Previous Showing 11-19 of 19 results.

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