A185201 - OEIS

%I #21 Jul 19 2024 21:39:18

%S 5,11,9,33,11,21,27,29,71,57,53,39,137,29,53,83,23,33,57,27,113,71,53,

%T 303,321,249,107,261,53,17,81,119,47,513,237,179,123,123,173,27,203,

%U 137,119,77,119,147,83,47,183,161,333,339,611,579

%N 10^n - second largest prime less than 10^n.

%D 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.

%H Robert Israel, <a href="/A185201/b185201.txt">Table of n, a(n) for n = 1..1000</a>

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

%e a(1) = 5 because precprime(10) = 7, and precprime(6) = 5.

%e From _M. F. Hasler_, Jul 19 2024: (Start)

%e Further examples: (where pp = prevprime = A151799)

%e     n |   pp(pp(10^n))  | a(n)

%e   ----+-----------------+------

%e     1 |               5 |   5

%e     2 |              89 |  11

%e     3 |             991 |   9

%e     4 |            9967 |  33

%e     5 |           99989 |  11

%e     6 |          999979 |  21

%e     7 |         9999973 |  27

%e     8 |        99999971 |  29

%e     9 |       999999929 |  71

%e    10 |      9999999943 |  57

%e    11 |     99999999947 |  53

%e    12 |    999999999961 |  39

%e    13 |   9999999999863 | 137

%e    14 |  99999999999971 |  29

%e    15 | 999999999999947 |  53

%e (End)

%p seq(10^n - prevprime(prevprime(10^n)),n=1..100); # _Robert Israel_, May 28 2017

%t Table[10^n - NextPrime[10^n, -2], {n,1,50}] (* _G. C. Greubel_, Jun 24 2017 *)

%o (PARI) apply( {A185201(n)=10^n-precprime(precprime(10^n)-1)}, [1..66]) \\ _M. F. Hasler_, Jul 19 2024

%Y Cf. A033874.

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

%K nonn

%O 1,1

%A _Washington Bomfim_, Jan 24 2012