A152819 "Upper primes" (see A152754).

2, 11, 37, 41, 43, 47, 59, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 227, 229, 233, 239, 251, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727

Offset: 1

Author

Vladimir Shevelev, Dec 13 2008

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2490

Crossrefs

Cf. A152754.

Programs

Mathematica

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 *)

PARI

a000695(n) = fromdigits(binary(n), 4);
half1(n) = { my(t=1, s=0); while(n>0, s += (n%2)*t; n \= 4; t *= 2); (s); }; \\ A059905
half2(n) = { my(t=1, s=0); while(n>0, s += ((n%4)>=2)*t; n \= 4; t *= 2); (s); }; \\ A059906
isok(n) = isprime(n) && a000695(half1(n)) < a000695(half2(n)); \\ Michel Marcus, Dec 15 2018

Extensions

More terms from Michel Marcus, Dec 15 2018