A272717 - OEIS

%I #36 May 02 2024 04:24:18

%S 1,5,7,17,35,46,56,148,187,190,256,551,553,1033,1751,1976,2696,3116,

%T 3364,5353,5893,8063,9548,10640,24655,77992

%N Numbers k such that (65*10^k + 691)/9 is prime.

%C For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).

%C a(27) > 10^5.

%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 72w99</a>.

%e 5 is in this sequence because (65*10^5+691)/9 = 722299 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 149;

%e a(2) = 5, 722299;

%e a(3) = 7, 72222299;

%e a(4) = 17, 722222222222222299;

%e a(5) = 35, 722222222222222222222222222222222299, etc.

%t Select[Range[0, 100000], PrimeQ[(65*10^#+691)/9] &]

%o (PARI) is(n)=ispseudoprime((65*10^n+691)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,2

%A _Robert Price_, Aug 11 2016