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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A152754.

Sequence in context: A353979 A084098 A263547 * A297406 A178138 A220888

Adjacent sequences: A152816 A152817 A152818 * A152820 A152821 A152822

Keyword

nonn

Author

Vladimir Shevelev, Dec 13 2008

Extensions

More terms from Michel Marcus, Dec 15 2018

Status

approved