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A350592 Integers m such that b(m) := 20^m*(5^(m+1) - 1)/4 + (20^m - 1)/19 is a prime.

%I A350592 #17 Dec 21 2024 01:04:46
%S A350592 2,4,5,7,9,13,85,222,249,1843
%N A350592 Integers m such that b(m) := 20^m*(5^(m+1) - 1)/4 + (20^m - 1)/19 is a prime.
%C A350592 b(m) = Sum_{i=0..2m} 2^(m - |m - i|)*10^i.
%C A350592 a(11) > 5000. - _Michael S. Branicky_, Jun 07 2022
%C A350592 a(11) > 50000. - _Michael S. Branicky_, Dec 21 2024
%e A350592 m            b(m)          n    a(n)
%e A350592 --   -------------------   --   ----
%e A350592 0             1
%e A350592 1            121
%e A350592 2           12421          1     2
%e A350592 3          1248421
%e A350592 4         124968421        2     4
%e A350592 5        12499368421       3     5
%e A350592 6       1249987368421
%e A350592 7      124999747368421     4     7
%e A350592 8     12499994947368421
%e A350592 9    1249999898947368421   5     9
%t A350592 Select[Range[250], PrimeQ[20^# * (5^(# + 1) - 1)/4 + (20^# - 1)/19] &] (* _Amiram Eldar_, Jan 08 2022 *)
%o A350592 (Python)
%o A350592 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 A350592 Cf. A002477, A016134, A260802.
%K A350592 nonn,base,more
%O A350592 1,1
%A A350592 _Ya-Ping Lu_, Jan 07 2022