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A152819 "Upper primes" (see A152754).

%I A152819 #10 Dec 16 2018 06:40:56
%S A152819 2,11,37,41,43,47,59,131,137,139,149,151,157,163,167,173,179,181,191,
%T A152819 227,229,233,239,251,521,523,541,547,557,563,569,571,577,587,593,599,
%U A152819 601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727
%N A152819 "Upper primes" (see A152754).
%H A152819 Vincenzo Librandi, <a href="/A152819/b152819.txt">Table of n, a(n) for n = 1..2490</a>
%t A152819 fh[n_,h_] := If[h==1, Mod[n,2], If[Mod[n,4]>=2,1,0]]; half[n_, h_ ] := Module[{t=1, s=0, m=n}, While[m>0, s += fh[m,h]*t; m=Quotient[m,4]; t *= 2]; s]; mb[n_] := FromDigits[Riffle[IntegerDigits[n, 2], 0], 2]; aQ[n_] := PrimeQ[n] && mb[half[ n,1]] < mb[half[n, 2]]; Select[Range[730], aQ] (* _Amiram Eldar_, Dec 16 2018 from the PARI code *)
%o A152819 (PARI) a000695(n) = fromdigits(binary(n), 4);
%o A152819 half1(n) = { my(t=1, s=0); while(n>0, s += (n%2)*t; n \= 4; t *= 2); (s); }; \\ A059905
%o A152819 half2(n) = { my(t=1, s=0); while(n>0, s += ((n%4)>=2)*t; n \= 4; t *= 2); (s); }; \\ A059906
%o A152819 isok(n) = isprime(n) && a000695(half1(n)) < a000695(half2(n)); \\ _Michel Marcus_, Dec 15 2018
%Y A152819 Cf. A152754.
%K A152819 nonn
%O A152819 1,1
%A A152819 _Vladimir Shevelev_, Dec 13 2008
%E A152819 More terms from _Michel Marcus_, Dec 15 2018