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 11-19 of 19 results.

A108329 Integers k such that 10^k - 27 is prime.

Original entry on oeis.org

2, 4, 7, 14, 20, 22, 29, 31, 40, 80, 85, 224, 767, 952, 3592, 4016, 4187, 9239, 17684, 20716, 30791
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

Keywords

Comments

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99973".
The next term, if one exists, is > 100000. - Robert Price, Apr 25 2011

Examples

			k = 7 is a term because 10^7 - 27 = 10000000 - 27 = 9999973, which is prime.

Links

Crossrefs

Cf. A089675, A095714, A092767, A176987.

Extensions

a(18)-a(19) from Kamada data by Robert Price, Dec 10 2010
a(20)-a(21) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010

A093172 Primes of the form 10^n - 3.

Original entry on oeis.org

7, 97, 997, 99999999999999997
Offset: 1

Views

Author

Rick L. Shepherd, Mar 26 2004

Keywords

Comments

Primes of the form (9*10^n - 27)/9. - Vincenzo Librandi, Nov 16 2010
Also primes of the form 9*R_n - 2, where R_n is the repunit (A002275) of length n.
The next term has 140 digits.
a(n) = 10^A089675(n) - 3 = 10^(A056662(n) + 1) - 3. - Farideh Firoozbakht, Nov 27 2013

Links

Crossrefs

Subsequence of A020471 and hence of A030096.
Cf. A002275, A056662, A089675.

Programs

  • Mathematica
    Do[If[PrimeQ[10^n - 3], Print[10^n - 3]], {n, 100}] (* Farideh Firoozbakht, Nov 27 2013 *)
Select[Table[FromDigits[PadLeft[{7},n,9]],{n,25}],PrimeQ] (* Harvey P. Dale, Dec 12 2020 *)
  • PARI
    for(n=1,9, if(isprime(p=10^n-3), print1(p", "))) \\ Charles R Greathouse IV, Dec 13 2024

Extensions

Name shortened and old name moved to comments by Alex Ratushnyak, Apr 26 2012

A101398 Numbers k such that 4*10^k-3 is prime.

Original entry on oeis.org

1, 2, 14, 20, 30, 44, 66, 260, 872, 8846, 26744, 57506, 98472, 106892
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

Keywords

Comments

See Kamada link for search limit and prime vs. PRP status.
a(14) > 10^5. - Robert Price, Mar 17 2015
a(15) > 2*10^5. - Robert Price, Oct 02 2015

Examples

			k = 1, 2, 14, 20 are members since 37, 397, 399999999999997 and 399999999999999999997
are prime numbers.

Links

Crossrefs

Cf. A089675, A101849.

Programs

  • Mathematica
    Do[ If[ PrimeQ[4*10^n - 3], Print[n]], {n, 0, 10000}]
  • PARI
    for(n=1, 1e4, if(isprime(4*10^n-3), print1(n", "))) \\ Altug Alkan, Oct 02 2015

Formula

a(n) = A101849(n) + 1.

Extensions

a(11)-a(12) from Kamada data by Robert Price, Dec 13 2010
a(13) from Kamada data by Robert Price, Mar 17 2015
a(14) from Robert Price, Oct 02 2015

A108331 Integers k such that 10^k - 87 is prime.

Original entry on oeis.org

2, 1800, 2368, 15328
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

Keywords

Comments

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99913".
a(5) > 10^5. - Tyler NeSmith, Jul 26 2021

Examples

			k = 2 is a term because 10^2 - 87 = 100 - 87 = 13, which is prime.

Links

Crossrefs

Cf. A089675, A095714, A092767.

Extensions

a(4) from Kamada data by Robert Price, Dec 13 2010
Edited by Ray Chandler, Dec 23 2010

A108332 Integers k such that 10^k - 89 is prime.

Original entry on oeis.org

2, 3, 637, 2349, 29455, 175093
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

Keywords

Comments

637 corresponds to a certified prime (Primo 2.2.0 beta). - Ryan Propper, Nov 06 2005
No additional terms < 40000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "9w11".

Examples

			k = 3 is a term because 10^3 - 89 = 1000 - 89 = 911, which is prime.

Links

Crossrefs

Cf. A089675, A095714, A092767.

Programs

  • Mathematica
    Do[If[PrimeQ[10^n - 89], Print[n]], {n, 2, 10^4}] (* Ryan Propper, Nov 06 2005 *)

Extensions

a(5) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010
a(6) from Riley Fisher, Oct 09 2023

A105080 Number of distinct prime divisors of 10000^n - 3.

Original entry on oeis.org

2, 2, 2, 4, 4, 2, 3, 4, 4, 5, 4, 5, 4, 4, 4, 4, 5, 3, 5, 4, 5, 3, 4, 8, 4, 3, 6, 5, 5, 3, 7, 5, 3, 5, 1, 4, 6, 5
Offset: 1

Views

Author

Parthasarathy Nambi, Apr 06 2005

Keywords

Examples

			The number of distinct prime divisors of 10000^1 - 3 is 2, so the first term is 2.

Links

Crossrefs

Cf. A089675, A105068, A105069.

Programs

  • Mathematica
    PrimeNu[#]&/@(10000^Range[10]-3) (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Feb 05 2023 *)

Formula

A105080(n) = A105068(4n) = A105069(2n). - Robert G. Wilson v, Apr 08 2005

Extensions

More terms from Robert G. Wilson v, Apr 08 2005

A108493 Integers n such that 10^n-57 is prime.

Original entry on oeis.org

2, 7, 10, 11, 17, 19, 39, 49, 50, 61, 95, 106, 187, 196, 849, 889, 6436, 7370, 14446, 19647, 34399, 39922, 81297, 84305
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jul 06 2005

Keywords

Comments

Numbers corresponding to terms 849 and 889 are certified primes. (Primo 2.2.0 beta) - Ryan Propper, Jul 13 2005
No additional terms <100000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99943".

Examples

			n = 7 is a member because: 10^7-57 = 10000000-57 = 9999943, which is prime.

Links

Crossrefs

Cf. A089675, A095714, A092767, A108327, A108328, A108329, A108330, A108331, A108332, A177417.

Extensions

a(17)-a(19) from Kamada data by Robert Price, Dec 10 2010
a(20) from Kamada data by Robert Price, Dec 14 2010
a(21)-a(22) from Robert Price, Dec 15 2010
Edited by Ray Chandler, Dec 23 2010
a(23-24)=81297,84305 from Robert Price, May 29 2011

A235710 Composite numbers k such that sum of the proper divisors of k is a power of 10.

Original entry on oeis.org

14, 124, 194, 1324, 1994, 13324, 133324, 1130324, 1333324, 13333324, 62496048, 133333324, 92782317392, 7453083061400, 657119364560000, 671701040192960, 199999999999999994, 1333333333333333324
Offset: 1

Views

Author

Farideh Firoozbakht, Mar 17 2014

Keywords

Comments

Composite numbers k such that reversal(sigma(k)-k) = 1.
If k is prime, then sum of the proper divisors of k is 10^0.
Terms include 2*(10^A089675(k)-3) and 4*(10^A055557(k)-7)/3 for all k >= 1.

Examples

			sigma(14)-14 = 1+2+7 = 10, sigma(124)-124 = 1+2+4+31+62 = 100.

Crossrefs

Cf. A000203, A004086, A055557, A089675.

Programs

  • Mathematica
    r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[If[!PrimeQ[n]&& r[DivisorSigma[1,n]-n]==1, Print[n]],{n, 200000000}]

Extensions

a(13) from Giovanni Resta, Mar 21 2014
Edited and a(14)-a(18) added by Max Alekseyev, May 24 2025

A108326 Integers n such that 10^n-17 is prime.

Original entry on oeis.org

2, 3, 6, 30, 40, 86, 128, 264, 639, 912, 1932, 4650, 5038, 7410, 19041
Offset: 1

Views

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Jun 30 2005

Keywords

Comments

Terms 639 and 912 correspond to certified primes (Primo 2.2.0 beta). - Ryan Propper, Jul 12 2005
No other terms < 40000.
See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "99983".
No other terms < 100,000. - Robert Price, Mar 03 2011

Examples

			If n = 3 we have 10^3-17 = 1000-17 = 983, which is prime.

Links

Crossrefs

Cf. A089675, A095714, A092767.

Extensions

a(14)-a(15) from Robert Price, Dec 11 2010
Edited by Ray Chandler, Dec 23 2010
Previous Showing 11-19 of 19 results.

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