|
%I #13 May 18 2024 11:31:46
%S 1,2,5,7,8,11,17,61,73,89,197,233,308,2096,3170,8003,15014,16166,
%T 26021,55748,102533,171601
%N Numbers k such that (536*10^k - 23)/9 is prime.
%C For k>1, numbers k such that the digits 59 followed by k-1 occurrences of the digit 5 followed by the digit 3 is prime (see Example section).
%C a(23) > 2*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 595w3</a>.
%e 2 is in this sequence because (536*10^2 - 23)/9 = 5953 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 593;
%e a(2) = 2, 5953;
%e a(3) = 5, 5955553;
%e a(4) = 7, 595555553;
%e a(5) = 8, 5955555553; etc.
%t Select[Range[0, 100000], PrimeQ[(536*10^# - 23)/9] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard,changed
%O 1,2
%A _Robert Price_, Nov 05 2017
%E a(21)-a(22) from _Robert Price_, Feb 23 2020
|
