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 1-4 of 4 results.

A099552 a(n) is the smallest positive integer such that the concatenation of the first n terms is divisible by n.

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 5, 6, 1, 10, 2, 12, 5, 14, 5, 6, 8, 10, 15, 20, 7, 6, 18, 24, 25, 6, 32, 32, 3, 10, 1, 12, 41, 34, 5, 6, 8, 46, 33, 20, 34, 36, 21, 24, 30, 36, 36, 48, 23, 50, 56, 44, 34, 42, 30, 48, 9, 26, 4, 60, 44, 34, 33, 60, 65, 28, 16, 32, 66, 20, 29, 44, 78, 48, 75, 52, 9, 8, 37
Offset: 1

Views

Author

David Wasserman, Oct 21 2004

Keywords

Links

Crossrefs

Cf. A051883, A073893, A083161, A100769.

Programs

  • Mathematica
    spi[{ctn_,n_,a_}]:=Module[{k=1},While[Mod[ctn*10^IntegerLength[k]+k,n+1] != 0,k++];{ctn*10^IntegerLength[k]+k,n+1,k}]; NestList[spi,{1,1,1},80][[All,3]] (* Harvey P. Dale, Nov 30 2022 *)
  • PARI
    num = 1; print(1); for (n = 2, 9, c = 10*num%n; d = n - c; print(d); num = 10*num + d); for (n = 10, 90, c = 10*num%n; d = n - c; if (d < 10, print(d); num = 10*num + d, c = 100*num%n; d = n - c; if (d < 10, d = d + n); print(d); num = 100*num + d));

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

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

A096099 a(0) = 1, a(n) = least number such that the concatenation of all terms through a(n) is divisible by prime(n).

Original entry on oeis.org

1, 2, 3, 5, 5, 2, 13, 25, 8, 22, 16, 26, 35, 35, 11, 26, 48, 58, 6, 46, 4, 77, 83, 29, 33, 187, 61, 78, 81, 23, 183, 15, 22, 68, 8, 137, 84, 178, 99, 7, 71, 82, 142, 241, 133, 71, 56, 19, 32, 318, 157, 199, 303, 16, 201, 201, 213, 257, 355, 229, 365, 379, 345, 27, 52, 19, 272
Offset: 0

Views

Author

Amarnath Murthy, Jun 24 2004

Keywords

Comments

Related sequence: numbers k such that a(k) > prime(k): 7, 21, 22, 25, 30, 37, 43, 49, 52, 58, 60, 61, 62 ... (E.g., 7 would be a term since a(7) = 25 > prime(7) = 17.) [edited by Jon E. Schoenfield, Nov 19 2018]

Examples

			a(7) = 25 as the concatenation a(1),a(2),...,a(6),a(7) = 1235521325 == 0 (mod 17), prime(7) = 17.

Links

Crossrefs

Cf. A073893.

Programs

  • Mathematica
    s = "1"; Print[s]; Do[k = 1; While[Mod[ToExpression[s <> ToString[k]], Prime[n]] != 0, k++ ]; Print[k]; s = s <> ToString[k], {n, 1, 100}] (* Ryan Propper, Sep 03 2005 *)

Extensions

a(10)-a(66) from Ryan Propper, Sep 03 2005
Showing 1-4 of 4 results.

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