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.

A183176 Numbers k such that (10^(2k+1) + 12*10^k - 1)/3 is prime.

Original entry on oeis.org

1, 3, 7, 11, 13, 17, 29, 31, 33, 77, 933, 1555, 11758, 117707
Offset: 1

Views

Author

Ray Chandler, Dec 28 2010

Keywords

Comments

a(14) > 100000. - Robert Price, Dec 29 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) + 12*10^n - 1)/3], Print[n]], {n, 3000}]
  • PARI
    is(n)=ispseudoprime((10^(2*n+1)+12*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077790(n) - 1)/2.

Extensions

a(14) from Robert Price, Oct 30 2023

A332137 a(n) = (10^(2n+1)-1)/3 + 4*10^n.

Original entry on oeis.org

7, 373, 33733, 3337333, 333373333, 33333733333, 3333337333333, 333333373333333, 33333333733333333, 3333333337333333333, 333333333373333333333, 33333333333733333333333, 3333333333337333333333333, 333333333333373333333333333, 33333333333333733333333333333, 3333333333333337333333333333333
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A183176 = {1, 3, 7, 11, 13, 17, 29, 31, ...} for the indices of primes.

Crossrefs

Cf. (A077790-1)/2 = A183176: 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. A332127 .. A332197 (variants with different repeated digit 2, ..., 9).
Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332137 := n -> (10^(2*n+1)-1)/3+4*10^n;
  • Mathematica
    Array[ (10^(2 # + 1)-1)/3 + 4*10^# &, 15, 0]
  • PARI
    apply( {A332137(n)=10^(n*2+1)\3+4*10^n}, [0..15])
    
  • Python
    def A332137(n): return 10**(n*2+1)//3+4*10**n

Formula

a(n) = 3*A138148(n) + 7*10^n = A002277(2n+1) + 4*10^n.
G.f.: (7 - 404*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.
Showing 1-2 of 2 results.