A287102 Numbers k such that (10^(4*k+1)*37 + 10^(2*k)*(-99) - 73)/99 is prime (k > 0).

1, 9, 441, 2980

Offset: 1

Author

Mikk Heidemaa, May 19 2017

Keywords

• nonn
• hard
• more
• base

Comments

Or '37'||...'37'||'2'||'73'...||'73' in decimal form is prime (as a string, it consists of a middle '2' with the prefix composed of '37' concatenated k times, and the suffix composed of '73' concatenated k times).

a(5), if it exists, is greater than 58079. - Robert Price, May 03 2018

Examples

			9 is a term because (10^(4*9+1)*37 + 10^(2*9)*(-99) - 73)/99 = 3737373737373737372737373737373737373 (prime). As a string, it consists of a middle '2' with the prefix '373737373737373737' ('37' concatenated 9 times) and the suffix '737373737373737373' ('73' concatenated 9 times).
		

Crossrefs

Cf. A173954, A239479.

Programs

Mathematica

ParallelMap[ If[ PrimeQ[ (10^(4*#+1)*37+10^(2*#)*(-99)-73)/99], #, Nothing]&, Range[3000]]