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%I #17 Dec 21 2024 01:04:46
%S 2,4,5,7,9,13,85,222,249,1843
%N Integers m such that b(m) := 20^m*(5^(m+1) - 1)/4 + (20^m - 1)/19 is a prime.
%C b(m) = Sum_{i=0..2m} 2^(m - |m - i|)*10^i.
%C a(11) > 5000. - _Michael S. Branicky_, Jun 07 2022
%C a(11) > 50000. - _Michael S. Branicky_, Dec 21 2024
%e m b(m) n a(n)
%e -- ------------------- -- ----
%e 0 1
%e 1 121
%e 2 12421 1 2
%e 3 1248421
%e 4 124968421 2 4
%e 5 12499368421 3 5
%e 6 1249987368421
%e 7 124999747368421 4 7
%e 8 12499994947368421
%e 9 1249999898947368421 5 9
%t Select[Range[250], PrimeQ[20^# * (5^(# + 1) - 1)/4 + (20^# - 1)/19] &] (* _Amiram Eldar_, Jan 08 2022 *)
%o (Python)
%o from sympy import isprime; {print(m, end = ', ') for m in range(2000) if isprime(20**m*(5**(m+1) - 1)//4 + (20**m - 1)//19)}
%Y Cf. A002477, A016134, A260802.
%K nonn,base,more
%O 1,1
%A _Ya-Ping Lu_, Jan 07 2022