A185201 10^n - second largest prime less than 10^n.

5, 11, 9, 33, 11, 21, 27, 29, 71, 57, 53, 39, 137, 29, 53, 83, 23, 33, 57, 27, 113, 71, 53, 303, 321, 249, 107, 261, 53, 17, 81, 119, 47, 513, 237, 179, 123, 123, 173, 27, 203, 137, 119, 77, 119, 147, 83, 47, 183, 161, 333, 339, 611, 579

Offset: 1

Author

Washington Bomfim, Jan 24 2012

Keywords

• nonn

Examples

			a(1) = 5 because precprime(10) = 7, and precprime(6) = 5.
From _M. F. Hasler_, Jul 19 2024: (Start)
Further examples: (where pp = prevprime = A151799)
    n |   pp(pp(10^n))  | a(n)
  ----+-----------------+------
    1 |               5 |   5
    2 |              89 |  11
    3 |             991 |   9
    4 |            9967 |  33
    5 |           99989 |  11
    6 |          999979 |  21
    7 |         9999973 |  27
    8 |        99999971 |  29
    9 |       999999929 |  71
   10 |      9999999943 |  57
   11 |     99999999947 |  53
   12 |    999999999961 |  39
   13 |   9999999999863 | 137
   14 |  99999999999971 |  29
   15 | 999999999999947 |  53
(End)
		

References

• D. E. Knuth, The Art of Computer Programming, Second Edition, Vol. 2, Seminumerical Algorithms, Chapter 4.5.4 Factoring into Primes, Table 1, Page 390, Addison-Wesley, Reading, MA, 1981.

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033874.

Cf. A003618 (largest prime < 10^n), A151799 (prevprime function).

Programs

Maple

seq(10^n - prevprime(prevprime(10^n)),n=1..100); # Robert Israel, May 28 2017

Mathematica

Table[10^n - NextPrime[10^n, -2], {n,1,50}] (* G. C. Greubel, Jun 24 2017 *)

PARI

apply( {A185201(n)=10^n-precprime(precprime(10^n)-1)}, [1..66]) \\ M. F. Hasler, Jul 19 2024

Formula

a(n) = 10^n - precprime(precprime(10^n)-1)