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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A332194 a(n) = 10^(2n+1) - 1 - 5*10^n.

Original entry on oeis.org

4, 949, 99499, 9994999, 999949999, 99999499999, 9999994999999, 999999949999999, 99999999499999999, 9999999994999999999, 999999999949999999999, 99999999999499999999999, 9999999999994999999999999, 999999999999949999999999999, 99999999999999499999999999999, 9999999999999994999999999999999
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183185 = {14, 22, 36, 104, 1136, ...} for the indices of primes.

Crossrefs

Cf. (A077782-1)/2 = A183185: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332114 .. A332184 (variants with different repeated digit 1, ..., 8).
Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Programs

  • Maple
    A332194 := n -> 10^(n*2+1)-1-5*10^n;
  • Mathematica
    Array[ 10^(2 # + 1) -1 -5*10^# &, 15, 0]
  • PARI
    apply( {A332194(n)=10^(n*2+1)-1-5*10^n}, [0..15])
    
  • Python
    def A332194(n): return 10**(n*2+1)-1-5*10^n

Formula

a(n) = 9*A138148(n) + 4*10^n = A002283(2n+1) - 5*A011557(n).
G.f.: (4 + 505*x - 1400*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.

A077782 Numbers k such that (10^k - 1) - 5*10^floor(m/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

29, 45, 73, 209, 2273, 35729, 50897
Offset: 1

Views

Author

Patrick De Geest, Nov 16 2002

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			29 is a term because (10^29 - 1) - 5*10^14 = 99999999999999499999999999999.
		

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^n - 5*10^Floor[n/2] - 1], Print[n]], {n, 3, 50900, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183185(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018
Showing 1-2 of 2 results.