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%I #8 Feb 23 2024 11:03:31
%S 4,8,12,20,24,28,32,36,40,44,52,56,60,68,72,76,84,88,92,96,100,104,
%T 108,116,120,124,128,132,136,140,148,152,156,160,164,168,172,180,184,
%U 188,196,200,204,212,216,220,224,228,232,236,244,248,252,260,264,268,276
%N Numbers k such that A007814(k) is a prime number.
%C Numbers whose binary representation has a prime number of trailing 0's.
%C a(n)-1 is the sequence of numbers whose binary representation has a prime number of trailing 1's.
%C Numbers of the form (2^(p+1))*k + 2^p = 2^p * (2*k + 1), where p is prime and k >= 0.
%C All the terms are divisible by 4.
%C The asymptotic density of this sequence is Sum_{p prime} 1/2^(p+1) = 0.20734125492555583012... = A051006 / 2.
%H Amiram Eldar, <a href="/A370596/b370596.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[300], PrimeQ[IntegerExponent[#, 2]] &]
%o (PARI) is(n) = isprime(valuation(n, 2));
%Y Cf. A007814, A051006, A359794.
%Y Subsequences: A017113, A051062.
%K nonn,easy
%O 1,1
%A _Amiram Eldar_, Feb 23 2024
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