A090457 Primes prime(k) having fewer binary 1's than k.

17, 257, 277, 293, 307, 401, 449, 577, 641, 643, 653, 673, 677, 709, 1031, 1033, 1039, 1091, 1093, 1129, 1153, 1217, 1297, 1409, 1543, 1553, 1601, 1607, 1609, 1613, 2053, 2063, 2081, 2083, 2087, 2089, 2099, 2113, 2179, 2309, 2341, 2371, 2593, 2609, 2633, 2647

Offset: 1

Author

Reinhard Zumkeller, Dec 01 2003

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A004676, A072439, A014499, A007088, A090433, A090455, A090456.

Programs

Mathematica

seq[len_] := Module[{s = {}, p = 2, k = 1, c = 0}, While[c < len, If[Greater @@ DigitCount[{k, p}, 2, 1], c++; AppendTo[s, p]]; k++; p = NextPrime[p]]; s]; seq[50] (* Amiram Eldar, Jul 18 2023 *)
Prime[#]&/@Select[Range[500],DigitCount[#,2,1]>DigitCount[Prime[#],2,1]&] (* Harvey P. Dale, Apr 19 2024 *)

PARI

isok(k) = hammingweight(prime(k)) < hammingweight(k);
lista(nn) = for(n=1, nn, if (isok(n), print1(prime(n), ", "))); \\ Michel Marcus, Feb 05 2016

Formula

A090455(a(n)) > 0.