%I #20 Aug 14 2023 06:28:30

%S 201,40001,500001,6000001,70000001,800000001,100000000001,

%T 1100000000001,12000000000001,130000000000001,1400000000000001,

%U 15000000000000001,160000000000000001,1700000000000000001,18000000000000000001,190000000000000000001,2000000000000000000001

%N Composite numbers of the form k*10^k + 1.

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

%H M. Abramowitz and I. A. Stegun, eds., <a href="https://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%e For k=2, 2*10^2 + 1 = 201 = 3*67.

%e For k=4, 4*10^4 + 1 = 40001 = 13*17*181.

%p with(numtheory):for k from 1 to 100 do: n:=k*10^k +1:if type(n,prime) = false then print(n):else fi:od:

%t Select[Table[k*10^k+1, {k, 1, 20}], CompositeQ] (* _Amiram Eldar_, Aug 14 2023 *)

%Y Intersection of A002808 and A064748.

%Y Subsequence of A005381.

%Y Cf. A216347.

%K nonn

%O 1,1

%A _Michel Lagneau_, Mar 01 2010

%E a(16)-a(17) added and name corrected by _Amiram Eldar_, Aug 14 2023