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 1-6 of 6 results.

A291884 Complement of A039691.

Original entry on oeis.org

19, 28, 29, 37, 38, 39, 46, 47, 48, 49, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 119, 128, 129, 137, 138, 139, 146, 147, 148, 149, 155, 156, 157, 158, 159, 164, 165
Offset: 1

Views

Author

Michel Marcus, Sep 05 2017

Keywords

Examples

			46*11 = 506 while 64*11 = 704 where 704 is not the reverse of 506, so 46 is a term.

Crossrefs

Cf. A039691.

Programs

  • PARI
    isok(n) = my(d = digits(n), y = n*11); fromdigits(Vecrev(digits(y))) != fromdigits(Vecrev(d))*11;

A242407 Numbers such that in ternary representation all pairs of adjacent digits have sums not greater than 2.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 9, 10, 11, 12, 13, 18, 19, 20, 27, 28, 29, 30, 31, 33, 36, 37, 38, 39, 40, 54, 55, 56, 57, 58, 60, 81, 82, 83, 84, 85, 87, 90, 91, 92, 93, 94, 99, 100, 101, 108, 109, 110, 111, 112, 114, 117, 118, 119, 120, 121, 162, 163, 164, 165, 166, 168
Offset: 1

Views

Author

Reinhard Zumkeller, May 13 2014

Keywords

Comments

A242400(a(n)) = 0;
A242399(a(n)) = 4*a(n);
numbers m, such that in ternary arithmetic no carry occurs, when 3*m is added to m.

Examples

			Initial terms and their ternary representations, cf. A007089:
.  0 1 2  3  4  6   9  10  11  12  13  18  19  20   27   28   29   30 ..
.  0 1 2 10 11 20 100 101 102 110 111 200 201 202 1000 1001 1002 1010 ..

Links

Crossrefs

Cf. A242408 (complement), A003714, A039691, A007089.

Programs

  • Haskell
    a242407 n = a242407_list !! (n-1)
a242407_list = filter ((== 0) . a242400) [0..]
  • Mathematica
    Select[Range[0,200],Max[Total/@Partition[IntegerDigits[#, 3],2,1]]<3&] (* Harvey P. Dale, Jan 08 2023 *)

A059632 Carryless product 11 X n base 10.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 109, 220, 231, 242, 253, 264, 275, 286, 297, 208, 219, 330, 341, 352, 363, 374, 385, 396, 307, 318, 329, 440, 451, 462, 473, 484, 495, 406, 417, 428, 439, 550, 561, 572, 583
Offset: 0

Views

Author

Henry Bottomley, Feb 19 2001

Keywords

Comments

a(n) <= 11*n; a(m) = 11*m iff m is a term of A039691. - Reinhard Zumkeller, Jul 05 2014

Examples

			a(19)=109 since we have 11 X 19 = carryless sum of 100, 90, 10 and 9 =109

Links

Crossrefs

Cf. A001477 for carryless 1 X n, A004520 for carryless 2 X 10 base 10, A055120 for carryless 9 X n, A008592 for carryless 10 X n.
Cf. A048724 carryless 3Xn in base 2, A242399 carryless 4Xn in base 3.
Cf. A008593.

Programs

  • Haskell
    a059632 n = foldl (\v d -> 10 * v + d) 0 $
                  map (flip mod 10) $ zipWith (+) ([0] ++ ds) (ds ++ [0])
            where ds = map (read . return) $ show n
-- Reinhard Zumkeller, Jul 05 2014

A248014 Numbers m such that A247796(m) < m.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115
Offset: 1

Views

Author

Reinhard Zumkeller, Oct 08 2014

Keywords

Comments

Numbers containing at least one pair of adjacent digits with sum <= 9 in decimal representation.

Links

Crossrefs

Cf. A248013 (complement).

Programs

  • Haskell
    a248014 n = a248014_list !! (n-1)
a248014_list = filter (\x -> a247796 x < x) [0..]

Formula

A247796(a(n)) < a(n).
A168046(a(n)) = 1. [Editor's note: This is obviously wrong. Certainly another sequence number was meant. Please edit or inform us if you find the correct reference.]
a(n) = A039691(n+10) up to a(64) = 118, but a(65) = 119 is not in A039691. - M. F. Hasler, Jan 26 2018

A298639 Numbers k such that the digital sum of k and the digital root of k have the same parity.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114
Offset: 1

Views

Author

J. Stauduhar, Jan 26 2018

Keywords

Comments

Numbers k such that A113217(k) = A179081(k).
Complement of A298638.
Agrees with A039691 until a(65): A039691(65) = 109 is not in this sequence.

Links

Crossrefs

Cf. A007953, A010888, A113217, A179081, A298638, A039691.

Programs

  • Mathematica
    fQ[n_] := Mod[Plus @@ IntegerDigits@n, 2] == Mod[Mod[n -1, 9] +1, 2]; fQ[0] = True; Select[ Range[0, 104], fQ] (* Robert G. Wilson v, Jan 26 2018 *)
  • PARI
    dr(n)=if(n, (n-1)%9+1);
isok(n) = (sumdigits(n) % 2) == (dr(n) % 2); \\ Michel Marcus, Jan 26 2018
  • PARI
    is(n)=bittest(sumdigits(n)-(n-1)%9,0)||!n \\ M. F. Hasler, Jan 26 2018
  • Python
    #Digital sum of n.
def ds(n):
  if n < 10:
    return n
  return n % 10 + ds(n//10)
def A298639(term_count):
  seq = []
  m = 0
  n = 1
  while n <= term_count:
    s = ds(m)
    r = ((m - 1) % 9) + 1 if m else 0
    if s % 2 == r % 2:
      seq.append(m)
      n += 1
    m += 1
  return seq
print(A298639(100))

A084011 Digit reversal of 11*n, divided by 11.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 31, 41, 51, 61, 71, 81, 82, 2, 12, 22, 32, 42, 52, 62, 72, 73, 83, 3, 13, 23, 33, 43, 53, 63, 64, 74, 84, 4, 14, 24, 34, 44, 54, 55, 65, 75, 85, 5, 15, 25, 35, 45, 46, 56, 66, 76, 86, 6, 16, 26, 36, 37, 47, 57, 67, 77, 87, 7, 17, 27, 28, 38, 48, 58
Offset: 1

Views

Author

Amarnath Murthy, May 23 2003

Keywords

Examples

			For n = 13, A004086(13*11)/11 = 341/11 = 31. So, a(13) = 31. - _Indranil Ghosh_, Jan 10 2017

Links

Crossrefs

Cf. A004086, A007091.
Cf. A039691 (n such that a(n) = A004086(n)).

Programs

  • Mathematica
    a[n_] := Module[{aux = IntegerDigits[11*n]},Sum[aux[[i]]*10^(i - 1), {i, 1, Length[aux]}]/11]; Table[a[n], {n, 100}] (* José María Grau Ribas, Feb 16 2010 *)
  • Python
    def A084011(n):
     return int(str(11*n)[::-1])/11 # Indranil Ghosh, Jan 10 2017

Formula

a(n) = A004086(11*n)/11. - Indranil Ghosh, Jan 10 2017
Showing 1-6 of 6 results.

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