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A254441 Numbers k such that (41*10^k + 49)/9 is prime.

%I A254441 #45 May 31 2024 22:11:19
%S A254441 2,3,6,20,26,38,51,119,155,218,446,486,1211,1319,1338,1365,1575,5106,
%T A254441 7019,9503,9695,14304,15417,17765,24222,25500,26306,35238,93207
%N A254441 Numbers k such that (41*10^k + 49)/9 is prime.
%C A254441 For terms k > 1, numbers that begin with the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 61 are prime (see Example section).
%C A254441 a(30) > 2*10^5.
%H A254441 Alois P. Heinz, <a href="/A254441/b254441.txt">Table of n, a(n) for n = 1..29</a>
%H A254441 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A254441 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 45w61</a>.
%e A254441 3 is in this sequence because (41*10^3 + 49)/9 = 4561 is prime.
%e A254441 Initial terms and associated primes:
%e A254441 a(1) = 2, 461;
%e A254441 a(2) = 3, 4561;
%e A254441 a(3) = 6, 4555561;
%e A254441 a(4) = 20, 455555555555555555561;
%e A254441 a(5) = 26, 455555555555555555555555561, etc.
%t A254441 Select[Range[0, 100000], PrimeQ[(41*10^# + 49)/9] &]
%o A254441 (PARI) is(n)=ispseudoprime((41*10^n + 49)/9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A254441 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A254441 nonn,more
%O A254441 1,1
%A A254441 _Robert Price_, Apr 17 2016