A254441 - OEIS

%I #45 May 31 2024 22:11:19

%S 2,3,6,20,26,38,51,119,155,218,446,486,1211,1319,1338,1365,1575,5106,

%T 7019,9503,9695,14304,15417,17765,24222,25500,26306,35238,93207

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

%C 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 a(30) > 2*10^5.

%H Alois P. Heinz, <a href="/A254441/b254441.txt">Table of n, a(n) for n = 1..29</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 45w61</a>.

%e 3 is in this sequence because (41*10^3 + 49)/9 = 4561 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 461;

%e a(2) = 3, 4561;

%e a(3) = 6, 4555561;

%e a(4) = 20, 455555555555555555561;

%e a(5) = 26, 455555555555555555555555561, etc.

%t Select[Range[0, 100000], PrimeQ[(41*10^# + 49)/9] &]

%o (PARI) is(n)=ispseudoprime((41*10^n + 49)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more

%O 1,1

%A _Robert Price_, Apr 17 2016