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 1-10 of 79 results. Next

A087100 A000225 (2^n - 1) interlaced with A008593 (11n).

Original entry on oeis.org

0, 1, 11, 3, 22, 7, 33, 15, 44, 31, 55, 63, 66, 127, 77, 255, 88, 511, 99, 1023, 110, 2047, 121, 4095, 132, 8191, 143, 16383, 154, 32767, 165, 65535, 176, 131071, 187, 262143, 198, 524287, 209, 1048575, 220, 2097151, 231, 4194303, 242, 8388607, 253
Offset: 0

Views

Author

Jeremy Gardiner, Aug 10 2003

Keywords

Links

Crossrefs

Cf. A063914, A087098, A086848.

Programs

  • Mathematica
    Rest[With[{nn=30},Riffle[2^Range[0,nn]-1,11Range[0,nn]]]] (* Harvey P. Dale, Aug 15 2011 *)

Formula

From Chai Wah Wu, Feb 02 2021: (Start)
a(n) = 4*a(n-2) - 5*a(n-4) + 2*a(n-6) for n > 5.
G.f.: x*(22*x^3 + x^2 - 11*x - 1)/((x - 1)^2*(x + 1)^2*(2*x^2 - 1)). (End)

A008594 Multiples of 12.

Original entry on oeis.org

0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 36 ).
The positive terms are the differences of consecutive star numbers (A003154). - Mihir Mathur, Jun 07 2013
A089911(a(n)) = 0. - Reinhard Zumkeller, Jul 05 2013
a(1) = 12 is a primitive abundant number, thus all a(n), n >= 2, are nonprimitive abundant numbers. - Daniel Forgues, Sep 24 2016

Links

Crossrefs

Subsequence of A072065 and A121032.
Cf. A003154, A008588, A008592, A008593, A008606, A089911.

Programs

Formula

From Vincenzo Librandi, Jun 11 2011: (Start)
a(n) = 12*n.
a(n) = 2*a(n-1) - a(n-2) for n > 1.
G.f.: 12*x/(1-x)^2. (End)
a(n) = A003154(n) - A003154(n-1). - Mihir Mathur, Jun 07 2013
From Elmo R. Oliveira, Apr 10 2025: (Start)
E.g.f.: 12*x*exp(x).
a(n) = 2*A008588(n) = A008606(n)/2. (End)

A121031 Multiples of 11 containing an 11 in their decimal representation.

Original entry on oeis.org

11, 110, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2112, 2211, 3113, 3311, 4114, 4411, 5115, 5511, 6116, 6611, 7117, 7711, 8118, 8811, 9119, 9911, 11000, 11011, 11022, 11033, 11044, 11055, 11066, 11077, 11088, 11099, 11110
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 21 2006

Keywords

Links

Crossrefs

Cf. A121041, A008593, A011531, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.

Programs

  • Mathematica
    Select[11*Range[1100],MemberQ[Partition[IntegerDigits[#],2,1],{1,1}]&] (* Harvey P. Dale, Feb 16 2014 *)
Select[11Range[1100],SequenceCount[IntegerDigits[#],{1,1}]>0&] (* Harvey P. Dale, Jun 14 2024 *)
  • PARI
    is(n)=if(n%11, return(0)); while(n>10, if(n%100==11, return(1)); n\=10); 0 \\ Charles R Greathouse IV, Feb 12 2017

Formula

a(n) ~ 11n. - Charles R Greathouse IV, Feb 12 2017

A061470 First (leftmost) digit - second digit + third digit - fourth digit .... = 1.

Original entry on oeis.org

1, 10, 21, 32, 43, 54, 65, 76, 87, 98, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 210, 221, 232, 243, 254, 265, 276, 287, 298, 320, 331, 342, 353, 364, 375, 386, 397, 430, 441, 452, 463, 474, 485, 496, 540, 551, 562, 573, 584, 595, 650, 661, 672, 683
Offset: 1

Views

Author

Amarnath Murthy, May 05 2001

Keywords

Examples

			221 is in the sequence since 2-2+1 = 1.

Links

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.
Cf. A225693.

Programs

  • Haskell
    a061470 n = a061470_list !! (n-1)
a061470_list = filter ((== 1) . a225693) [0..]
-- Reinhard Zumkeller, Aug 08 2014
  • Mathematica
    d[n_]:=IntegerDigits[n]; a[n_]:=Differences[Reverse[Total/@{Take[d[n],{1,-1,2}],Take[d[n],{2,-1,2}]}]]; Select[Range[690],a[#]=={1} &] (* Jayanta Basu, May 18 2013 *)
Select[Range[1000],Total[Times@@@Partition[Riffle[IntegerDigits[#],{1,-1},{2,-1,2}],2]]==1&] (* Harvey P. Dale, May 24 2021 *)

Formula

A225693(a(n)) = 1. - Reinhard Zumkeller, Aug 08 2014

Extensions

More terms from Robert G. Wilson v, May 10 2001 and from Larry Reeves (larryr(AT)acm.org), May 14 2001

A061870 Numbers such that |first digit - second digit + third digit - fourth digit ...| = 1.

Original entry on oeis.org

1, 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 100, 111, 120, 122, 131, 133, 142, 144, 153, 155, 164, 166, 175, 177, 186, 188, 197, 199, 210, 221, 230, 232, 241, 243, 252, 254, 263, 265, 274, 276, 285, 287, 296, 298, 320, 331, 340, 342
Offset: 1

Views

Author

Robert G. Wilson v, May 10 2001

Keywords

Comments

Multiples of 11 plus or minus 1. If 11k+1 is a perfect square (see A219257) then a(n) is the square root of 11k+1. [Gary Detlefs, Feb 22 2010]

Examples

			120 is in the sequence since |1-2+0| = 1.

Links

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.
Subsequence of A175885.

Programs

  • Mathematica
    fQ[n_] := Abs[Plus @@ (((-1)^Range[Floor[Log[10, n] + 1]])*IntegerDigits@n)] == 1; Select[ Range@342, fQ@# &]
  • PARI
    altsum(v)=sum(i=1,#v,v[i]*(-1)^i)
is(n)=abs(altsum(digits(n)))==1 \\ Charles R Greathouse IV, May 21 2014
  • Python
    def ok(n): return abs(sum(int(di)*(-1)**i for i, di in enumerate(str(n)))) == 1
print([k for k in range(343) if ok(k)]) # Michael S. Branicky, Jan 26 2023

A060978 |First digit - second digit + third digit - fourth digit ...| = 10.

Original entry on oeis.org

109, 208, 219, 307, 318, 329, 406, 417, 428, 439, 505, 516, 527, 538, 549, 604, 615, 626, 637, 648, 659, 703, 714, 725, 736, 747, 758, 769, 802, 813, 824, 835, 846, 857, 868, 879, 901, 912, 923, 934, 945, 956, 967, 978, 989, 1090, 1209, 1308, 1319, 1407
Offset: 1

Views

Author

Robert G. Wilson v, May 10 2001

Keywords

Links

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.

Programs

  • Mathematica
    Do[ a = IntegerDigits[ n ]; l = Length[ a ]; e = o = {}; Do[ o = Append[ o, a[ [ 2k - 1 ] ] ], {k, 1, l/2 + .5} ]; Do[ e = Append[ e, a[ [ 2k ] ] ], {k, 1, l/2} ]; If[ Abs[ Apply[ Plus, o ] - Apply[ Plus, e ] ] == 10, Print[ n ] ], {n, 1, 2000} ]
Select[Range[1500],Abs[Total[Times@@@Partition[Riffle[IntegerDigits[#],{1,-1},{2,-1,2}],2]]]==10&] (* Harvey P. Dale, Apr 13 2020 *)

A060980 |First digit - second digit + third digit - fourth digit ...| = 12.

Original entry on oeis.org

309, 408, 419, 507, 518, 529, 606, 617, 628, 639, 705, 716, 727, 738, 749, 804, 815, 826, 837, 848, 859, 903, 914, 925, 936, 947, 958, 969, 1409, 1508, 1519, 1607, 1618, 1629, 1706, 1717, 1728, 1739, 1805, 1816, 1827, 1838, 1849, 1904, 1915, 1926, 1937
Offset: 1

Views

Author

Robert G. Wilson v, May 10 2001

Keywords

Links

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.

Programs

  • Mathematica
    Do[ a = IntegerDigits[ n ]; l = Length[ a ]; e = o = {}; Do[ o = Append[ o, a[ [ 2k - 1 ] ] ], {k, 1, l/2 + .5} ]; Do[ e = Append[ e, a[ [ 2k ] ] ], {k, 1, l/2} ]; If[ Abs[ Apply[ Plus, o ] - Apply[ Plus, e ] ] == 12, Print[ n ] ], {n, 1, 2000} ]
Select[Range[2000],Abs[Total[Times@@@Partition[Riffle[IntegerDigits[#],{1,-1},{2,-1,2}],2]]]==12&] (* Harvey P. Dale, Sep 12 2017 *)

A060982 a(n) = Smallest nontrivial number k > 9 such that |first (leftmost) decimal digit of k - second digit + third digit - fourth digit ...| = n.

Original entry on oeis.org

11, 10, 13, 14, 15, 16, 17, 18, 19, 90, 109, 209, 309, 409, 509, 609, 709, 809, 909, 10909, 20909, 30909, 40909, 50909, 60909, 70909, 80909, 90909, 1090909, 2090909, 3090909, 4090909, 5090909, 6090909, 7090909, 8090909, 9090909, 109090909, 209090909, 309090909
Offset: 0

Views

Author

Robert G. Wilson v, May 10 2001

Keywords

Comments

Starting with 109, this sequence has the same terms as A061479 and A061882. - Georg Fischer, May 24 2022

Links

Crossrefs

Cf. A008593, A060978-A060980, A060982, A061470-A061479, A061870-A061882.

Programs

  • Mathematica
    m = 2; Do[ While[ a = IntegerDigits[ m ]; l = Length[ a ]; e = o = {}; Do[ o = Append[ o, a[ [ 2k - 1 ] ] ], {k, 1, l/2 + .5} ]; Do[ e = Append[ e, a[ [ 2k ] ] ], {k, 1, l/2} ]; Abs[ Apply[ Plus, o ] - Apply[ Plus, e ] ] != n, m++ ]; Print[ m ], {n, 1, 50} ]
  • Python
    def f(m): return abs(sum((-1)**i*int(d) for i, d in enumerate(str(m))))
def a(n):
    m = 10
    while f(m) != n: m += 1
    return m
print([a(n) for n in range(28)]) # Michael S. Branicky, Nov 10 2021
  • Python
    # faster version based on formula
def a(n):
    if n < 10: return [11, 10, 13, 14, 15, 16, 17, 18, 19, 90][n]
    q, r = divmod(n, 9)
    return int(str(r if r else 9) + "09"*(q if r else q-1))
print([a(n) for n in range(40)]) # Michael S. Branicky, Nov 10 2021

Formula

For n > 8, if r = 0, a(n) = 90..90, else a(n) = r09..09, where r = n mod 9 and 90 and 09, resp., occur ceiling(n/9) times. - Michael S. Branicky, Nov 10 2021

Extensions

a(39) and beyond from Michael S. Branicky, Nov 10 2021
Definition amended by Georg Fischer, May 24 2022

A061479 Smallest number m such that first digit - second digit + third digit - fourth digit ... (of m) = n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 109, 209, 309, 409, 509, 609, 709, 809, 909, 10909, 20909, 30909, 40909, 50909, 60909, 70909, 80909, 90909, 1090909, 2090909, 3090909, 4090909, 5090909, 6090909, 7090909, 8090909, 9090909, 109090909, 209090909
Offset: 0

Views

Author

Amarnath Murthy, May 05 2001

Keywords

Examples

			a(14) = 509 as 5-0+9 =14 and it is the smallest such number.

Crossrefs

Subsequence of A032945.
Cf. A225693, A008593, A060978-A060980, A060982, A061470-A061478, A061870-A061882.

Programs

  • Mathematica
    m = 0; Do[ While[ a = IntegerDigits[ m ]; l = Length[ a ]; e = o = {}; Do[ o = Append[ o, a[ [ 2k - 1 ] ] ], {k, 1, l/2 + .5} ]; Do[ e = Append[ e, a[ [ 2k ] ] ], {k, 1, l/2} ]; Abs[ Apply[ Plus, o ] - Apply [ Plus, e ] ] != n, m++ ]; Print[ m ], {n, 1, 50} ]

Extensions

More terms from Robert G. Wilson v, May 10 2001

A061882 a(n) = Smallest nontrivial number k > 9 such that first (leftmost) digit - second digit + third digit - fourth digit ... of k = n.

Original entry on oeis.org

11, 10, 20, 30, 40, 50, 60, 70, 80, 90, 109, 209, 309, 409, 509, 609, 709, 809, 909, 10909, 20909, 30909, 40909, 50909, 60909, 70909, 80909, 90909, 1090909, 2090909, 3090909, 4090909, 5090909, 6090909, 7090909, 8090909, 9090909, 109090909
Offset: 0

Views

Author

Larry Reeves (larryr(AT)acm.org), May 15 2001

Keywords

Comments

Starting with 109, this sequence has the same terms as A060982 and A061479. - Georg Fischer, May 24 2022

Crossrefs

Cf. A008593, A051885, A060978-A060980, A060982, A061470-A061479, A061870-A061882.

Programs

  • PARI
    a(n) = my(k=1,d=digits(k)); while (sum(k=1, #d, (-1)^(k+1)*d[k]) != n, k++; d=digits(k)); k; \\ Michel Marcus, May 24 2022

Extensions

Definition amended by Georg Fischer, May 24 2022
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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