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 1-3 of 3 results.

A089675 Numbers k such that 10^k - 3 is prime.

Original entry on oeis.org

1, 2, 3, 17, 140, 990, 1887, 3530, 5996, 13820, 21873, 26045, 87720, 232599, 480684, 538640
Offset: 1

Views

Author

Michael Gottlieb (mzrg(AT)verizon.net), Jan 05 2004

Keywords

Comments

Numbers k such that 9*R_k - 2 is a prime number, where R_k = 11...1 is the repunit (A002275) of length k.
If k is in the sequence (10^k-3 is prime) and m=3*(10^k-3) then phi(m)=reversal(m), i.e., m is in the sequence A069215. - Farideh Firoozbakht, Dec 25 2004
No further terms for k <= 407197, see Kamada link.

Examples

			10^2 - 3 = 97 is a prime number (in fact all terms are the largest less than 10^k).

Links

Crossrefs

Cf. A002275, A056662, A069215, A093172, A101700.

Programs

  • Mathematica
    m = 1000; For[n = 1, n < m, If[PrimeQ[10^n - 3], Print[n]]; n++]

Formula

a(n) = A056662(n) + 1.

Extensions

a(8) from Robert G. Wilson v, Jan 14 2004
a(9) and a(10) from Gabriel Cunningham (gcasey(AT)mit.edu), Mar 06 2004
a(11) from Gabriel Cunningham (gcasey(AT)mit.edu), Mar 13 2004
a(12) from Henri Lifchitz.
Edited by Patrick De Geest, Dec 28 2004
Edited by Ray Chandler, Dec 23 2010
a(15) from Paul Bourdelais, Jan 06 2021
a(16) from Paul Bourdelais, Jan 28 2021

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

A057674 Primes -p+2^n with smallest p prime, arising in A057674.

Original entry on oeis.org

-3, 2, 5, 13, 29, 61, 109, 251, 509, 1021, 2029, 4093, 8179, 16381, 32749, 65519, 131059, 262139, 524269, 1048573, 2097133, 4194301, 8388571, 16777213, 33554371, 67108859, 134217649, 268435367, 536870909, 1073741783, 2147483629, 4294967291, 8589934513, 17179869143
Offset: 0

Views

Author

Labos Elemer, Oct 19 2000

Keywords

Examples

			n=1, 2^1=2. If 2,3,5 are subtracted from 2, then 0,-1 and -3 arise, of which -3 is a prime so a(1)=-3. n=11, 2048-p=q. At first p=29 gives the prime q=2029.

Crossrefs

Cf. A056206, A056208, A056662, A057674.
Showing 1-3 of 3 results.

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

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