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 41-43 of 43 results.

A309358 Numbers k such that 10^k + 1 is a semiprime.

Original entry on oeis.org

4, 5, 6, 7, 8, 19, 31, 53, 67, 293, 586, 641, 922, 2137, 3011
Offset: 1

Views

Author

Hugo Pfoertner, Jul 29 2019

Keywords

Comments

a(16) > 12000.
10^k + 1 is composite unless k is a power of 2, and it can be conjectured that it is composite for all k > 2, cf. A038371 and A185121. - M. F. Hasler, Jul 30 2019
Suppose k is odd. Then k is a term if and only if (10^k+1)/11 is prime. - Chai Wah Wu, Jul 31 2019

Examples

			a(1) = 4 because 10^4 + 1 = 10001 = 73*137.

Crossrefs

Cf. A003021, A038371, A046413, A057934, A062397, A092559.
Odd terms in sequence: A001562.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019
  • Mathematica
    Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* Vincenzo Librandi, Jul 31 2019 *)

A065983 Palindromes whose digit sum is 4.

Original entry on oeis.org

4, 22, 121, 202, 1111, 2002, 10201, 11011, 20002, 101101, 110011, 200002, 1002001, 1010101, 1100011, 2000002, 10011001, 10100101, 11000011, 20000002, 100020001, 100101001, 101000101, 110000011, 200000002, 1000110001, 1001001001
Offset: 1

Views

Author

Henry Bottomley, Dec 10 2001

Keywords

Comments

There are ceiling(k/2) terms with k digits and so floor(n^2/4) terms with fewer than k digits. Writing the terms as a vertical column and then blanking zeros produces a narrow triangle with upward chevrons.

Crossrefs

Cf. A062397 and A066138 for digit sums of 2 and 3.

A107285 a(n) = 5*401*(10^n + 1).

Original entry on oeis.org

4010, 22055, 202505, 2007005, 20052005, 200502005, 2005002005, 20050002005, 200500002005, 2005000002005, 20050000002005, 200500000002005, 2005000000002005, 20050000000002005, 200500000000002005, 2005000000000002005, 20050000000000002005, 200500000000000002005
Offset: 0

Views

Author

Reinhard Zumkeller, May 20 2005

Keywords

Examples

			a(4) = 5*401*10001 = 20052005 = A106605(38).

Links

Crossrefs

Cf. A062397, A106605.

Programs

  • Mathematica
    2005(10^Range[0,20]+1) (* or *) LinearRecurrence[{11,-10},{4010,22055},20] (* Harvey P. Dale, Sep 06 2016 *)
  • PARI
    my(x='x+O('x^18)); Vec(2005*(2-11*x)/((10*x-1)*(x-1))) \\ Elmo R. Oliveira, Jun 16 2025

Formula

a(n) = 2005*A062397(n).
From Elmo R. Oliveira, Jun 16 2025: (Start)
G.f.: 2005*(2-11*x)/((1-x)*(1-10*x)).
E.g.f.: 2005*exp(x)*(1 + exp(9*x)).
a(n) = 10*a(n-1) - 18045.
a(n) = 11*a(n-1) - 10*a(n-2). (End)

Extensions

More terms from Elmo R. Oliveira, Jun 16 2025
Previous Showing 41-43 of 43 results.

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

Content is available under The OEIS End-User License Agreement.