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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A183180 Numbers k such that (7*10^(2k+1) - 18*10^k - 7)/9 is prime.

Original entry on oeis.org

0, 1, 7, 13, 58, 129, 253, 1657, 2244, 2437, 7924, 9903, 11899, 18157, 18957, 23665, 105609
Offset: 1

Views

Author

Ray Chandler, Dec 28 2010

Keywords

Comments

a(17) > 10^5. - Robert Price, Jun 23 2017
0 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the near-repdigit palindrome 777...77577...777 with 0 occurrences of the digit 7. - Robert Price, Jun 23 2017

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) - 18*10^n - 7)/9], Print[n]], {n, 3000}]
  • PARI
    is(n)=ispseudoprime((7*10^(2*n+1)-18*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077785(n) - 1)/2.

Extensions

a(16) from Robert Price, Jun 23 2017
a(17) from Robert Price, Oct 12 2023

A332175 a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.

Original entry on oeis.org

5, 757, 77577, 7775777, 777757777, 77777577777, 7777775777777, 777777757777777, 77777777577777777, 7777777775777777777, 777777777757777777777, 77777777777577777777777, 7777777777775777777777777, 777777777777757777777777777, 77777777777777577777777777777, 7777777777777775777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183180 = {0, 1, 7, 13, 58, 129, 253, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077785-1)/2 = A183180: indices of primes.
Cf. A138148 (cyclops numbers with binary digits only).
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
    A332175 := n -> 7*(10^(n*2+1)-1)/9 - 2*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 2*10^# &, 15, 0]
  • PARI
    apply( {A332175(n)=10^(n*2+1)\9*7-2*10^n}, [0..15])
  • Python
    def A332175(n): return 10**(n*2+1)//9*7-2*10^n

Formula

a(n) = 7*A138148(n) + 5*10^n.
G.f.: (5 + 202*x - 900*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) - 18*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020
Showing 1-2 of 2 results.

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

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