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%I #27 Jul 30 2024 07:30:23
%S 2,4,6,10,70,82,143,150,220,413,426,816,5497,6649,7429,7728,7891,8248,
%T 14567,15522,17935,24942,37415,123773
%N k such that either 2^k + k - 3 or 2^k + k - 2 is prime.
%C Numbers of this form can be represented in the numeral system described in A235860 with k - 1 ones followed to the right by k - 1 twos or k ones followed to the right by k - 1 twos, like this: 1, 12, 112, 1122, 11122, 111222, 1111222, ... (1, 3, 4, 8, 9, 17, 18, ... in decimal) and are the least numbers that need one more digit to be represented than any of their predecessors.
%C The corresponding sequence of primes starts 3, 17, 67, 1031, 1180591620717411303491, ...
%t fQ[n_] := PrimeQ[2^n + n - If[ OddQ@ n, 2, 3]]; Select[ Range@ 30000, fQ]
%o (PARI) isok(n) = isprime(2^n + n - 3) || isprime(2^n + n - 2); \\ _Michel Marcus_, Feb 13 2014
%Y Cf. A235860, A236547.
%K nonn,more
%O 1,1
%A _Robin Garcia_, Feb 13 2014
%E a(21)-a(22) from _Robert G. Wilson v_, Mar 03 2014
%E a(23) from _Michael S. Branicky_, May 01 2023
%E a(24) from _Michael S. Branicky_, Jul 30 2024
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