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.

A145851 Primes of the form k followed by k 9's.

Original entry on oeis.org

19, 49999, 599999, 1799999999999999999, 2099999999999999999999, 289999999999999999999999999999
Offset: 1

Views

Author

Lekraj Beedassy, Oct 21 2008

Keywords

Comments

Corresponding k, which cannot be multiples of 3, are in A174352. The next term has 176 digits, too large to include here. - Rick L. Shepherd, Mar 22 2010

Crossrefs

Cf. A141311, A145852.
Cf. A174352. - Rick L. Shepherd, Mar 22 2010

Programs

  • Mathematica
    Select[Table[FromDigits[PadRight[{k},k+1,9]],{k,200}],PrimeQ] (* Harvey P. Dale, Jun 22 2022 *)
  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k*10^(k-1)-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 24 2020

Extensions

a(2) was 4999; corrected by Rick L. Shepherd, Mar 22 2010

A320256 k-digit primes with the same even digit repeated k-1 times and a single odd digit.

Original entry on oeis.org

3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 223, 227, 229, 443, 449, 661, 881, 883, 887, 2221, 4441, 4447, 6661, 8887, 22229, 44449, 88883, 444443, 444449, 666667, 888887, 22222223, 66666667, 88888883, 222222227, 444444443, 666666667, 888888883, 888888887
Offset: 1

Views

Author

Enrique Navarrete, Oct 08 2018

Keywords

Comments

For the resulting number to be prime, the rightmost digit must be the odd one. - Michel Marcus, Oct 11 2018

Examples

			3, 5, 7 are in the sequence for k = 1.
229 is in the sequence because it is a 3-digit prime with the first 3-1 digits repeating even (2) and the last digit odd (9). - _David A. Corneth_, Oct 10 2018

Links

Crossrefs

Cf. A055558, A068690, A105975, A141311, A154764.

Programs

  • Mathematica
    Join[{3, 5, 7}, Select[Flatten@ Table[{1, 3, 7, 9} + 10 FromDigits@ ConstantArray[k, n], {n, 9}, {k, Range[2, 8, 2]}], PrimeQ]] (* Michael De Vlieger, Oct 31 2018 *)
  • PARI
    first(n) = {n = max(n, 3); my(t = 3, res = List([3, 5, 7])); print1("3, 5, 7, "); for(i=1, oo, k=(10^i - 1) / 9; forstep(f = 2, 8, 2, forstep(d=1, 9, 2, c = 10 * f * k + d; if(isprime(c), print1(c", "); listput(res, c); t++; if(t>=n, return(res))))))} \\ David A. Corneth, Oct 10 2018

Extensions

More terms from Michel Marcus, Oct 10 2018

A145852 Primes of the form k followed by a 0 and k 9's.

Original entry on oeis.org

109, 2099, 409999, 1909999999999999999999, 2809999999999999999999999999999, 41099999999999999999999999999999999999999999, 7609999999999999999999999999999999999999999999999999999999999999999999999999999
Offset: 1

Views

Author

Lekraj Beedassy, Oct 21 2008

Keywords

Comments

Primes of the form k*10^(k+1) + 10^k - 1.

Crossrefs

Cf. A141311, A145851.

Programs

  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k*10^(k+1)+10^k-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 24 2020

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
Showing 1-4 of 4 results.

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