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 1-5 of 5 results.

A173768 a(n) = (4*10^n - 31)/9.

Original entry on oeis.org

1, 41, 441, 4441, 44441, 444441, 4444441, 44444441, 444444441, 4444444441, 44444444441, 444444444441, 4444444444441, 44444444444441, 444444444444441, 4444444444444441, 44444444444444441, 444444444444444441, 4444444444444444441, 44444444444444444441, 444444444444444444441
Offset: 1

Views

Author

Vincenzo Librandi, Feb 24 2010

Keywords

Links

Crossrefs

Cf. A093174.

Programs

  • Magma
    [(4*10^n-31)/9: n in [1..20]]; // Vincenzo Librandi, Aug 20 2014
  • Mathematica
    NestList[10#+31&,1,20] (* or *) Table[FromDigits[PadLeft[{1},n,4]],{n,20}] (* Harvey P. Dale, May 28 2013 *)
Table[(4 10^n - 31)/9, {n, 1, 30}] (* Vincenzo Librandi, Aug 20 2014 *)

Formula

a(n) = 10*a(n-1) + 31, n>1.
G.f.: x*(1+30*x)/((10*x-1)*(x-1)).
From Elmo R. Oliveira, Jun 19 2025: (Start)
E.g.f.: 3 + exp(x)*(4*exp(9*x) - 31)/9.
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)

A092675 Primes of the form 80*R_k + 1, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

881, 8888888888888888881, 8888888888888888888888888888888888888888888888888888888888888888888888888888881
Offset: 1

Views

Author

Rick L. Shepherd, Mar 02 2004

Keywords

Comments

Primes of the form 888...881.
The number of 8's in each term is given by the corresponding term of A056664 and so the first term too large to include above is 888...8881 (with 138 8's).
Primes of the form (8*10^k - 71)/9. - Vincenzo Librandi, Nov 16 2010

Links

Crossrefs

Cf. A056664 (corresponding k).
Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571.

Programs

  • Mathematica
    Select[Table[10 FromDigits[PadRight[{},n,8]]+1,{n,150}],PrimeQ] (* Harvey P. Dale, Aug 07 2019 *)

A109548 Primes of the form aaaa...aa1 where a is 1, 2, 3, 4 or 5.

Original entry on oeis.org

11, 31, 41, 331, 2221, 3331, 4441, 33331, 333331, 3333331, 33333331, 44444444441, 555555555551, 5555555555551, 222222222222222221, 333333333333333331, 1111111111111111111, 11111111111111111111111
Offset: 1

Views

Author

Roger L. Bagula, Jun 26 2005

Keywords

Links

Crossrefs

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

Programs

  • Mathematica
    d[n_] = Mod[n, 6] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 5}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{1,2,3,4,5},{i,2,80}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

Formula

d=1, 2, 3, 4, 5 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1

A109549 Primes of the form aaaa...aa1 where a is 6, 7, 8 or 9.

Original entry on oeis.org

61, 71, 661, 881, 991, 6661, 99991, 9999991, 6666666661, 7777777777771, 666666666666666661, 8888888888888888881, 77777777777777777771, 666666666666666666661, 6666666666666666666661, 77777777777777777777771
Offset: 1

Views

Author

Roger L. Bagula, Jun 26 2005

Keywords

Comments

Easy-to-remember large primes can be formed in this manner.

Links

Crossrefs

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

Programs

  • Mathematica
    d[n_] = If[5 + Mod[n, 6] > 0, 5 + Mod[n, 6], 1] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 4}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{6,7,8,9},{i,2,100}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

Formula

d=6, 7, 8, 9 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1

A109550 Primes of the form aaaa...aa1 where a is 3, 4, 5, 6 or 7.

Original entry on oeis.org

31, 41, 61, 71, 331, 661, 3331, 4441, 6661, 33331, 333331, 3333331, 33333331, 6666666661, 44444444441, 555555555551, 5555555555551, 7777777777771, 333333333333333331, 666666666666666661, 77777777777777777771
Offset: 1

Views

Author

Roger L. Bagula, Jun 26 2005

Keywords

Links

Crossrefs

Cf. A051200, A004022, A093176, A093177, A089346, A093174, A092571, A089345, A089347.

Programs

  • Mathematica
    d[n_] = If[2 + Mod[n, 6] > 0, 2 + Mod[n, 6], 1] a = Flatten[Table[Sum[d[k]*10^i, {i, 1, m}] + 1, {m, 1, 50}, {k, 1, 4}]] b = Flatten[Table[If[PrimeQ[a[[i]]] == True, a[[i]], {}], {i, 1, Length[a]}]]
Select[FromDigits/@Flatten[Table[PadLeft[{1},i,#]&/@{3,4, 5,6,7},{i,2,100}],1],PrimeQ[#]&] (* Vincenzo Librandi, Dec 12 2011 *)

Formula

d=3, 4, 5, 6, 7 a(n) = if prime then Sum[d*10^i, {i, 1, m}] + 1
Showing 1-5 of 5 results.

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