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.

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A183181 Numbers k such that (7*10^(2*k+1) - 9*10^k - 7)/9 is prime.

Original entry on oeis.org

4, 5, 8, 11, 1244, 1685, 2009, 14657, 15118, 20332, 50830, 75062
Offset: 1

Views

Author

Ray Chandler, Dec 28 2010

Keywords

References

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

Links

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

  • Mathematica
    Do[If[PrimeQ[(7*10^(2n + 1) - 9*10^n - 7)/9], Print[n]], {n, 3000}]
  • PARI
    is(n)=ispseudoprime((7*10^(2*n+1)-9*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077788(n) - 1)/2.

Extensions

a(10) from Robert Price, Oct 07 2023
a(11) from Robert Price, Oct 17 2023
a(12) from Robert Price, Dec 06 2023

A332176 a(n) = 7*(10^(2n+1)-1)/9 - 10^n.

Original entry on oeis.org

6, 767, 77677, 7776777, 777767777, 77777677777, 7777776777777, 777777767777777, 77777777677777777, 7777777776777777777, 777777777767777777777, 77777777777677777777777, 7777777777776777777777777, 777777777777767777777777777, 77777777777777677777777777777, 7777777777777776777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183181 = {4, 5, 8, 11, 1244, 1685, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077788-1)/2 = A183181: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332176 := n -> 7*(10^(n*2+1)-1)/9 - 10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 10^# &, 15, 0]
  • PARI
    apply( {A332176(n)=10^(n*2+1)\9*7-10^n}, [0..15])
  • Python
    def A332176(n): return 10**(n*2+1)//9*7-10^n

Formula

a(n) = 7*A138148(n) + 6*10^n.
G.f.: (6 + 101*x - 800*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.

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

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