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.

A083161 a(n) = (concatenation of the first n terms of A099552)/n.

Original entry on oeis.org

1, 6, 41, 308, 2465, 20542, 176075, 1540657, 13694729, 1232525611, 11204778282, 1027104675851, 9480966238625, 880375436443751, 8216837406808343, 77032850688828216, 725015065306618504, 68473645056736192045
Offset: 1

Views

Author

Amarnath Murthy, Apr 25 2003

Keywords

Crossrefs

Cf. A073893.

Extensions

Corrected and extended by David Wasserman, Oct 21 2004

A073893 a(10k) = 0 and if n is not a multiple of 10 then a(n) is the smallest positive integer such that the concatenation of the first n terms is a multiple of n.

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 5, 6, 1, 0, 8, 4, 9, 4, 5, 6, 25, 2, 15, 0, 15, 10, 28, 16, 25, 16, 28, 16, 13, 0, 14, 4, 22, 36, 5, 16, 35, 14, 47, 0, 16, 8, 42, 28, 35, 18, 49, 44, 27, 0, 42, 4, 26, 6, 45, 52, 53, 38, 62, 0, 44, 50, 25, 28, 15, 32, 43, 72, 29, 0, 61, 44, 45, 8, 25, 56, 82, 84, 85, 0
Offset: 1

Views

Author

Amarnath Murthy, Aug 17 2002

Keywords

Comments

Note that the concatenation of the first 10k terms is not necessarily a multiple of 10k.

Crossrefs

Cf. A051883, A073894, A099552.

Extensions

Edited and extended by David Wasserman, Oct 21 2004

A100769 Beginning with 1, least positive integer not occurring earlier such that the n-th partial concatenation is a multiple of n.

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 16, 8, 9, 10, 14, 12, 20, 26, 35, 36, 37, 44, 7, 40, 31, 22, 19, 28, 25, 32, 39, 56, 60, 70, 43, 52, 49, 30, 15, 48, 51, 58, 59, 120, 50, 64, 93, 88, 65, 86, 61, 168, 101, 100, 57, 68, 13, 84, 155, 104, 158, 54, 127, 80, 133, 38, 78, 144, 45, 138, 18, 76
Offset: 1

Views

Author

Amarnath Murthy, Nov 27 2004

Keywords

Examples

			a(7) = 16 as the concatenation 12365416 of first seven terms is a multiple of 7. No number less than 16 and more than 6 fits in.

Links

Crossrefs

Cf. A099552, A100770.

Programs

  • Mathematica
    a[1] = 1; a[n_] := a[n] = Block[{t = 1}, While[Mod[FromDigits@ Flatten[IntegerDigits /@ Join[Array[a, n - 1], {t}]], n] != 0 || MemberQ[Array[a, n - 1], t], t++]; t]; Array[a, 68] (* Giorgos Kalogeropoulos, May 07 2023 *)
  • PARI
    See Link section.

Extensions

More terms from Joshua Zucker, May 27 2005

A073894 a(0)=1; a(n) for n > 0 is the smallest number not used earlier such that the concatenation of a(0),...,a(n) is a multiple of n+1.

Original entry on oeis.org

1, 0, 2, 4, 5, 6, 9, 12, 15, 10, 11, 24, 25, 8, 30, 40, 41, 18, 28, 20, 27, 46, 31, 52, 50, 32, 38, 60, 61, 80, 55, 36, 44, 120, 45, 48, 78, 26, 64, 160, 93, 14, 23, 140, 95, 98, 21, 76, 51, 100, 56, 92, 84, 34, 85, 68, 3, 62, 115, 180, 81, 74, 88, 128, 75, 58, 72, 124, 134
Offset: 0

Views

Author

Amarnath Murthy, Aug 17 2002

Keywords

Comments

Does every nonnegative integer eventually appear?

Examples

			Concatenation of a(0),...,a(6) is 1024569, not used so far are 3, 7, 8, 10, 11, 12, ..., the smallest of these that appended to 1024569 gives a multiple of 8 is 12: 102456912 = 8*12807114, hence a(7) = 12.

Crossrefs

Cf. A100769, A099552, A051883, A073893.

Extensions

Edited and extended by Klaus Brockhaus, Mar 28 2006

A083804 a(1) = 1. If the (n-1)th partial concatenation is divisible by n then a(n) = 0. Otherwise, a(n) is the smallest positive number such that the n-th partial concatenation is divisible by n.

Original entry on oeis.org

1, 2, 0, 0, 0, 0, 3, 2, 1, 10, 0, 8, 16, 8, 15, 20, 9, 4, 24, 20, 13, 28, 25, 28, 25, 30, 32, 20, 9, 10, 27, 2, 16, 10, 5, 36, 26, 10, 33, 20, 33, 46, 26, 28, 30, 50, 4, 48, 13, 50, 3, 12, 12, 6, 30, 64, 53, 56, 61, 60, 69, 36, 12, 8, 65, 74, 66, 4, 44, 20, 3, 76, 31, 62, 75, 6, 85, 56
Offset: 1

Views

Author

Amarnath Murthy, May 08 2003

Keywords

Examples

			1,12,120,1200,12000,120000 1200003 etc. are multiples of 1,2,3,4,5,6 and 7 respectively.

Crossrefs

Cf. A083805.
Cf. A051883, A073894, A099552.

Extensions

Corrected and extended by David Wasserman, Nov 30 2004

A308830 a(n) is the smallest positive integer such that the concatenation, in base 2, of the first n terms is divisible by n.

Original entry on oeis.org

1, 2, 3, 4, 5, 2, 9, 8, 5, 2, 3, 20, 7, 14, 27, 16, 11, 30, 11, 20, 15, 22, 31, 24, 11, 14, 11, 20, 15, 10, 35, 32, 1, 26, 97, 92, 53, 18, 31, 56, 91, 10, 3, 12, 27, 30, 15, 48, 37, 78, 23, 108, 9, 6, 49, 8, 51, 54, 87, 60, 79, 26, 25, 64, 111, 122, 117, 28
Offset: 1

Views

Author

Rémy Sigrist, Jun 27 2019

Keywords

Comments

This sequence is the binary variant of A099552.

Examples

			The first terms, alongside the concatenation of the first n terms, both in decimal and in base 2, are:
  n   a(n)  bin(a(n))  K(n)      bin(K(n))
  --  ----  ---------  --------  --------------------------
   1     1          1         1                           1
   2     2         10         6                         110
   3     3         11        27                       11011
   4     4        100       220                    11011100
   5     5        101      1765                 11011100101
   6     2         10      7062               1101110010110
   7     9       1001    113001           11011100101101001
   8     8       1000   1808024       110111001011010011000
   9     5        101  14464197    110111001011010011000101
  10     2         10  57856790  11011100101101001100010110

Links

Crossrefs

Cf. A007814, A099552.

Programs

  • PARI
    See Links section.

Formula

a(2^k) = 2^k for any k >= 0.
A007814(a(n)) = A007814(n).
Showing 1-6 of 6 results.

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