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 1-8 of 8 results.

A099419 Numbers k such that 7*R_k - 6 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

2, 13, 20, 23, 31, 100, 241, 275, 925, 1067, 1369, 2065, 7163, 37963, 91856, 111706, 260198, 271757, 314564, 348724
Offset: 1

Views

Author

Robert G. Wilson v, Oct 14 2004

Keywords

Comments

Also numbers k such that (7*10^k - 61)/9 is prime.

Links

Crossrefs

Cf. A002275, A056688, A093176.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 7(10^n - 1)/9 - 6], Print[n]], {n, 0, 7000}]

Formula

a(n) = A056688(n) + 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Extensions

a(13) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(14)-a(15) from Erik Branger, Dec 19 2009
a(16) from Erik Branger, Jan 29 2011
a(17) from Erik Branger, Nov 26 2011
a(18) from Erik Branger, Mar 05 2012
a(19)-a(20) from Erik Branger, Sep 23 2016

A056688 Numbers k such that 70*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

1, 12, 19, 22, 30, 99, 240, 274, 924, 1066, 1368, 2064, 7162, 37962, 91855, 111705, 260197, 271756, 314563, 348723
Offset: 1

Views

Author

Robert G. Wilson v, Aug 10 2000

Keywords

Comments

Also numbers k such that (7*10^(k+1)-61)/9 is prime.

Links

Crossrefs

Cf. A002275, A093176, A099419.

Programs

  • Mathematica
    Do[ If[ PrimeQ[70*(10^n - 1)/9 + 1], Print[n]], {n, 0, 7000}]

Formula

a(n) = A099419(n) - 1.

Extensions

a(13) from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(14)-a(15) from Erik Branger, Dec 19 2009
a(16) from Erik Branger, Jan 29 2011
a(17) from Erik Branger, Nov 26 2011
a(18) from Erik Branger, Mar 05 2012
a(19)-a(20) from Erik Branger, Sep 23 2016

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 *)

A173806 a(n) = (7*10^n - 61)/9 for n > 0.

Original entry on oeis.org

1, 71, 771, 7771, 77771, 777771, 7777771, 77777771, 777777771, 7777777771, 77777777771, 777777777771, 7777777777771, 77777777777771, 777777777777771, 7777777777777771, 77777777777777771, 777777777777777771, 7777777777777777771, 77777777777777777771, 777777777777777777771
Offset: 1

Views

Author

Vincenzo Librandi, Feb 25 2010

Keywords

Links

Crossrefs

Cf. A093176.

Programs

  • Magma
    [(7*10^n-61)/9: n in [1..20]]; // Vincenzo Librandi, Jul 05 2012
  • Mathematica
    CoefficientList[Series[(1+60*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* Vincenzo Librandi, Jul 05 2012 *)

Formula

a(n) = 10*a(n-1) + 61 with n > 0, a(0)=-6.
From Vincenzo Librandi, Jul 05 2012: (Start)
G.f.: x*(1+60*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
E.g.f.: 6 + exp(x)*(7*exp(9*x) - 61)/9. - Elmo R. Oliveira, Sep 09 2024

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 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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