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 1-7 of 7 results.

A089345 Primes of the form identical even digits followed by a 1.

Original entry on oeis.org

41, 61, 661, 881, 2221, 4441, 6661, 6666666661, 44444444441, 222222222222222221, 666666666666666661, 8888888888888888881, 666666666666666666661, 6666666666666666666661, 4444444444444444444444444441
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2003

Keywords

Links

Crossrefs

Cf. A089346, A089347.

Programs

  • Mathematica
    Select[FromDigits/@Flatten[Table[Join[PadLeft[{n},i,n],{1}],{i,100},{n,2,9,2}],1],PrimeQ] (* Vincenzo Librandi, Dec 12 2011 *)

Extensions

More terms from Ray Chandler, Nov 07 2003

A089347 Primes of the form identical digits followed by a 1.

Original entry on oeis.org

11, 31, 41, 61, 71, 331, 661, 881, 991, 2221, 3331, 4441, 6661, 33331, 99991, 333331, 3333331, 9999991, 33333331, 6666666661, 44444444441, 555555555551, 5555555555551, 7777777777771, 222222222222222221, 333333333333333331
Offset: 1

Views

Author

Amarnath Murthy, Nov 05 2003

Keywords

Links

Crossrefs

Cf. A089345, A089346.

Programs

  • Mathematica
    Select[ FromDigits /@ Flatten[ Table[ PadLeft[{1}, i, # ] & /@ {1, 2, 3, 4, 5, 6, 7, 8, 9}, {i, 2, 18}], 1], PrimeQ[ # ] &] (* Robert G. Wilson v, Nov 15 2003 *)

Extensions

More terms from Ray Chandler and Robert G. Wilson v, Nov 07 2003

A091189 Primes of the form 20*R_k + 1, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

2221, 222222222222222221, 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221
Offset: 1

Views

Author

Rick L. Shepherd, Feb 22 2004

Keywords

Comments

Primes of the form 222...221.
The number of 2's in each term is given by the corresponding term of A056660 and so the first term too large to include above is 222...2221 (with 120 2's).

Links

Crossrefs

Cf. A056660 (corresponding k), A084832.
Cf. A051200, A004022, A093176, A093177, A089346.

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 1-7 of 7 results.

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