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 1-2 of 2 results.

A183175 Numbers k such that (10^(2k+1) + 6*10^k - 1)/3 is prime.

Original entry on oeis.org

1, 2, 17, 79, 118, 162, 177, 185, 240, 824, 1820, 2354, 134811
Offset: 1

Views

Author

Ray Chandler, Dec 28 2010

Keywords

Comments

a(13) > 10^5. - Robert Price, Apr 03 2016

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Crossrefs

Programs

  • Mathematica
    Do[If[PrimeQ[(10^(2n + 1) + 6*10^n - 1)/3], Print[n]], {n, 3000}]
  • PARI
    is(n)=ispseudoprime((10^(2*n+1)+6*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077784(n) - 1)/2.

Extensions

a(13) from Robert Price, Aug 03 2024

A332135 a(n) = (10^(2n+1)-1)/3 + 2*10^n.

Original entry on oeis.org

5, 353, 33533, 3335333, 333353333, 33333533333, 3333335333333, 333333353333333, 33333333533333333, 3333333335333333333, 333333333353333333333, 33333333333533333333333, 3333333333335333333333333, 333333333333353333333333333, 33333333333333533333333333333, 3333333333333335333333333333333
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A183175 = {1, 2, 17, 79, 118, 162, 177, ...} for the indices of primes.

Crossrefs

Cf. (A077784-1)/2 = A183175: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002277 (3*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332125 .. A332195 (variants with different repeated digit 2, ..., 9).
Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332135 := n -> (10^(2*n+1)-1)/3+2*10^n;
  • Mathematica
    Array[ (10^(2 # + 1)-1)/3 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332135(n)=10^(n*2+1)\3+2*10^n}, [0..15])
    
  • Python
    def A332135(n): return 10**(n*2+1)//3+2*10**n

Formula

a(n) = 3*A138148(n) + 5*10^n = A002277(2n+1) + 2*10^n.
G.f.: (5 - 202*x - 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
E.g.f.: exp(x)*(10*exp(99*x) + 6*exp(9*x) - 1)/3. - Stefano Spezia, Sep 24 2024
Showing 1-2 of 2 results.