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%I #15 Nov 02 2021 22:01:46
%S 5,7,13,19,23,31,41,43,53,61,71,79,89,101,137,139,157,163,173,179,193,
%T 223,229,233,263,271,281,283,293,349,383,419,433,449,461,463,491,509,
%U 547,563,577,593,601,607,617,643,677,701,733,751,757,761,773,797,811,821,853,857,863,881,887,911,937,941,967
%N Primes p such that (2^k)+p+(2^(k+1)) is also prime, where 2^k is the largest power of 2 smaller than p.
%C Primes p such that p + 3*A053644(p) is also prime. - _Robert Israel_, Jan 13 2016
%H Robert Israel, <a href="/A267289/b267289.txt">Table of n, a(n) for n = 1..10000</a>
%e p = 5: 4 + 5 + 8 = 17 (is prime).
%e p = 7: 4 + 7 + 8 = 19 (is prime).
%e p = 31: 16 + 31 + 32 = 79 (is prime).
%e p = 43: 32 + 43 + 64 = 139 (is prime).
%e p = 71: 64 + 71 + 128 = 263 (is prime).
%e p = 89: 64 + 89 + 128 = 281 (is prime).
%p select(t -> isprime(t) and isprime(t + 3*2^ilog2(t)), [seq(i,i=3..10^4,2)]); # _Robert Israel_, Jan 13 2016
%t Select[Prime@ Range@ 165, Function[k, PrimeQ[(2^k) + # + (2^(k + 1))]]@ Floor@ Log2@ # &] (* _Michael De Vlieger_, Jan 12 2016 *)
%t lp2Q[p_]:=Module[{k=Floor[Log[2,p]]},PrimeQ[2^k+p+2^(k+1)]]; Select[ Prime[ Range[200]],lp2Q] (* _Harvey P. Dale_, Nov 02 2021 *)
%K nonn
%O 1,1
%A _Emre APARI_, Jan 12 2016
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