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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A183179 Numbers n such that 7*(10^(2n+1)-1)/9 - 3*10^n is prime.

Original entry on oeis.org

2, 3, 6, 23, 36, 69, 561, 723, 3438, 4104, 9020, 13977, 19655, 32400
Offset: 1

Views

Author

Ray Chandler, Dec 28 2010

Keywords

Comments

Original name: Numbers n such that (7*10^(2n+1)-27*10^n-7)/9 is prime.
a(15) > 10^5. - Robert Price, Nov 23 2015

References

  • C. Caldwell and H. Dubner, The near repdigit primes A(n-k-1)B(1)A(k), especially 9(n-k-1)8(1)9(k), 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) - 27*10^n - 7)/9], Print[n]], {n, 3000}]
  • PARI
    for(n=1, 1e3, if(ispseudoprime((7*10^(2*n+1)-27*10^n-7)/9), print1(n, ", "))) \\ Altug Alkan, Nov 23 2015

Formula

a(n) = (A077781(n)-1)/2.

Extensions

a(14) from Robert Price, Nov 23 2015

A332174 a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

4, 747, 77477, 7774777, 777747777, 77777477777, 7777774777777, 777777747777777, 77777777477777777, 7777777774777777777, 777777777747777777777, 77777777777477777777777, 7777777777774777777777777, 777777777777747777777777777, 77777777777777477777777777777, 7777777777777774777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183179 = {2, 3, 6, 23, 36, 69, 561, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077781-1)/2 = A183179: 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
    A332174 := n -> 7*(10^(n*2+1)-1)/9 - 3*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 3*10^# &, 15, 0]
  • PARI
    apply( {A332174(n)=10^(n*2+1)\9*7-3*10^n}, [0..15])
  • Python
    def A332174(n): return 10**(n*2+1)//9*7-3*10^n

Formula

a(n) = 7*A138148(n) + 4*10^n.
G.f.: (4 + 303*x - 1000*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.: (1/9)*exp(x)*(70*exp(99*x) - 27*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020
Showing 1-2 of 2 results.

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