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.

Previous Showing 11-16 of 16 results.

A136024 Largest prime factor of odd composites less than 10^n.

Original entry on oeis.org

3, 31, 331, 3331, 33331, 333331, 3333331, 33333331, 333333313, 3333333323, 33333333329, 333333333323, 3333333333301, 33333333333323, 333333333333307, 3333333333333301, 33333333333333323
Offset: 1

Views

Author

Enoch Haga, Dec 12 2007

Keywords

Comments

Last instance of the largest prime factor of odd N <= 10^n-1 associated with A136021.
This sequence is not the same as A051200. E.g., A051200(9)=333333331 is not prime and is different from a(9)=333333313. However, if A051200(n) is prime, then a(n)=A051200(n).

Examples

			a(1)=31 because it is the largest factor of odd N <= 10^2-1. The value of odd N where this factor first occurs is 3*31 = 93.

Crossrefs

Cf. A051200, A136021.

Programs

  • Mathematica
    a[n_]:=NextPrime[10^n/3,-1]; Array[a,17] (* Stefano Spezia, Aug 31 2025 *)
  • PARI
    a(n)=precprime(10^n\3)

Formula

a(n) = precprime(10^n/3) = A007917((10^n-1)/3). - Max Alekseyev, Sep 29 2015

Extensions

Clarified and extended by Charles R Greathouse IV, Oct 11 2009

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

A055559 Primes of the form 2999...999.

Original entry on oeis.org

2, 29, 2999, 2999999, 29999999, 29999999999999999999, 2999999999999999999999999999, 29999999999999999999999999999999999999999999, 29999999999999999999999999999999999999999999999999999999
Offset: 1

Views

Author

Labos Elemer, Jul 10 2000

Keywords

Comments

a(9)=29999999999999999999999999999999999999999999999999999999. - Vincenzo Librandi, Aug 07 2010
The next term (a(10)) has 208 digits, and a(11) has 1312 digits. - Harvey P. Dale, Jan 22 2023

Examples

			3*10^k - 1 is prime for k = 0, 1, 3, 6, 7, 19, ... (A056703). k gives the number of 9's in these numbers.

Crossrefs

Cf. A051200, A056703, A056703.

Programs

  • Mathematica
    Select[Table[FromDigits[PadRight[{2}, n, 9]], {n, 60}], PrimeQ] (* Harvey P. Dale, Jan 22 2023 *)

Formula

a(n) = A198698(A056703(n)) = 3*10^A056703(n) - 1. - Amiram Eldar, Mar 16 2025

Extensions

Erroneous Formula entry removed by Jon E. Schoenfield, Jan 14 2018
Extended by Harvey P. Dale, Jan 22 2023

A321363 Single-digit odd primes and primes whose decimal expansion has the form iii...ij, where i and j are distinct odd digits.

Original entry on oeis.org

3, 5, 7, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97, 113, 331, 337, 557, 773, 991, 997, 1117, 3331, 5557, 11113, 11117, 11119, 33331, 77773, 99991, 111119, 333331, 333337, 555557, 3333331, 9999991, 11111117, 11111119, 33333331, 55555553, 55555559, 111111113
Offset: 1

Views

Author

Enrique Navarrete, Nov 07 2018

Keywords

Crossrefs

Subsequence of A030096.
Cf. A051200, A055558, A062353, A065582, A105975, A141311, A320256.

Programs

  • Mathematica
    s={3, 5, 7}; Do[Do[Do[k=m*(10^n-1)/9*10+j; If[j!=m && PrimeQ[k], AppendTo[s, k]], {j,1,9,2}], {m,1,9,2}], {n,1,8}]; s (* Amiram Eldar, Nov 08 2018 *)
  • PARI
    lista(nn) = {print1("3, 5, 7, "); for (n=1, nn, r = (10^n-1)/9; forstep (i=1, 9, 2, forstep(j=1, 9, 2, if (i != j, if (isprime(p=fromdigits(concat(digits(r*i), j))), print1(p, ", "));););););} \\ Michel Marcus, Nov 28 2018

Extensions

a(35)-a(42) from Amiram Eldar, Nov 08 2018
Previous Showing 11-16 of 16 results.

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