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.

A095714 Numbers k such that 9*R_k - 8 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

3, 5, 7, 33, 45, 105, 197, 199, 281, 301, 317, 1107, 1657, 3395, 35925, 37597, 64305, 80139, 221631
Offset: 1

Views

Author

Alonso del Arte, Jul 07 2004

Keywords

Comments

Also numbers k such that 10^k - 9 is a prime.

Examples

			a(2) = 5, since 10^5 - 9 = 99991, which is prime.

Links

Crossrefs

Cf. A002275, A093177, A056696.

Programs

  • Mathematica
    Do[ If[ PrimeQ[10^n - 9], Print[n]], {n, 0, 7000}]

Formula

a(n) = A056696(n) + 1.

Extensions

a(12) - a(14) from Robert G. Wilson v, Oct 15 2004
a(15) - a(16) from Jason Earls, Jan 07 2008
a(17) - a(19) from Alexander Gramolin, May 13 2011
Edited by Ray Chandler, Feb 26 2012
Title corrected by Robert Price, Sep 06 2014

A093177 Primes of the form 90*R_k + 1, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

991, 99991, 9999991, 999999999999999999999999999999991, 999999999999999999999999999999999999999999991, 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
Offset: 1

Views

Author

Rick L. Shepherd, Mar 27 2004

Keywords

Comments

Primes of the form 10^k - 9 (k=3,5,7,...). - Vincenzo Librandi, Nov 16 2010

Links

Crossrefs

Cf. A056696 (corresponding k), A095714.

Formula

a(n) = 10^(A056696(n)+1) - 9 = 10^A095714(n) - 9.

Extensions

Edited by Ray Chandler, Feb 26 2012

A108537 Concatenation of palindrome k and its 10's complement is prime.

Original entry on oeis.org

1, 3, 7, 77, 99, 151, 161, 333, 707, 727, 737, 757, 949, 969, 989, 1441, 1551, 1771, 1881, 3003, 7227, 7667, 7997, 9009, 9339, 9999, 10001, 10101, 10701, 11111, 11611, 11711, 12221, 12921, 13231, 14341, 14841, 14941, 15851, 16661, 16961, 17071
Offset: 1

Views

Author

Jason Earls, Jul 25 2005

Keywords

Comments

Contains 10^k-1 for k in A056696, and (10^k-1)/9 for k in A108966. - Robert Israel, Jan 22 2019

Examples

			a(7)=161 because 1000-161 = 839 and 161839 is prime.

Links

Crossrefs

Cf. A056696, A108966.

Programs

  • Maple
    N:= 5: # for terms of <= N digits
digrev:= proc(n) local L,i;
   L:= convert(n,base,10);
   add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
Res:= 1,3,7,9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Res:= Res, seq(seq((i*10^(m-1)+j)*10^m + digrev(i*10^(m-1)+j), j=0..10^(m-1)-1),i=[1,3,7,9]);
  else
    m:= (d-1)/2;
    Res:= Res, seq(seq(seq((i*10^(m-1)+j)*10^(m+1)+y*10^m+digrev(i*10^(m-1)+j), y=0..9), j=0..10^(m-1)-1),i=[1,3,7,9]);
  fi
od:
filter:= proc(t) local r;
  r:= 10^(ilog10(t)+1)-t;
  isprime(t*10^(ilog10(r)+1)+r)
end proc:
select(filter, [Res]); # Robert Israel, Jan 22 2019
Showing 1-3 of 3 results.

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

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