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.

A068649 Primes in which a string of 9's is sandwiched between two 1's.

Original entry on oeis.org

11, 191, 19991, 199999991, 19999999999999999999999999999999999999991, 199999999999999999999999999999999999999999999999999999999999999999999999999999999999991
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term has 199 9's sandwiched between the starting and ending 1.

Examples

			11 is also a member in which a string of 0 9's is there between two one's.
		

Crossrefs

Programs

  • Maple
    a := 1:b := 9:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
  • Mathematica
    Select[Table[FromDigits[Join[{1}, Table[9, {i}], {1}]], {i, 0, 200}], PrimeQ]

Extensions

More terms from Sascha Kurz and Harvey P. Dale, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A056250 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 81 for n > 0.

Original entry on oeis.org

0, 1, 3, 7, 39, 85, 199, 729, 1459, 23671, 28629
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (180*10^n - 81)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.
Numbers corresponding to terms <= 1459 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			191 is prime, hence 1 is a term.
		

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 2000], PrimeQ[(180 10^# - 81) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+81)
    
  • PARI
    for(n=0,1500,if(isprime((180*10^n-81)/9),print1(n,",")))

Formula

a(n) = A082703(n-1) - 2 for n > 1.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Updated comments section and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014

A246804 Numbers k such that (10^(k+2) + 999) * 10^k + 1 is prime.

Original entry on oeis.org

1, 3, 15, 135, 645, 1373, 195317, 237249
Offset: 1

Views

Author

Serge Batalov, Nov 16 2014

Keywords

Comments

Or, indices of primes in the sequence of decimal palindromes 19991, 1099901, 100999001, 10009990001, ...
Or, numbers k such that there exists an "upside-down-Belphegor's primes" of length 2*k+3.

Crossrefs

Cf. A156166 (Belphegor's primes), A082703 (plateau primes 199...991).

Programs

  • Magma
    [n: n in [1..500] | IsPrime((10^(n+2)+999)*10^n+1)];
  • Maple
    A246804:=n->`if`(isprime((10^(n+2)+999)*10^n+1), n, NULL): seq(A246804(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014
  • Mathematica
    Select[Range[10^3], PrimeQ[(10^(# + 2) + 999)*10^# + 1] &]
  • PARI
    for( n=1,9999, ispseudoprime((10^(n+2)+999)*10^n+1) & print1(n","))
    
Showing 1-3 of 3 results.