A345335 Primes p such that A014499(k) / A000120(k) is an integer, where k = A000720(p).

2, 3, 5, 7, 19, 23, 29, 41, 53, 67, 71, 73, 83, 89, 97, 113, 131, 139, 193, 197, 211, 269, 281, 283, 311, 317, 337, 347, 349, 353, 359, 373, 389, 479, 503, 521, 523, 547, 563, 587, 593, 601, 647, 661, 691, 719, 739, 839, 857, 863, 881, 887, 929, 937, 983, 1013

Offset: 1

Author

Ctibor O. Zizka, Jun 14 2021

Keywords

• nonn
• base

Comments

A014499(k) / A000120(k) = 1 gives A072439.

Examples

			prime(8) = 19, A014499(8)/A000120(8) = 3, thus 19 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A000720, A014499, A071600, A072439.

Programs

Maple

R:= NULL: p:= 1: count:= 0:
for n from 1 while count < 100 do
  p:= nextprime(p);
  if convert(convert(p,base,2),`+`) mod convert(convert(n,base,2),`+`) = 0 then R:= R,p; count:= count+1 fi;
od:
R; # Robert Israel, Apr 21 2025

Mathematica

Select[Range[1000], PrimeQ[#] && Divisible @@ DigitCount[{#, PrimePi[#]}, 2, 1] &] (* Amiram Eldar, Jun 14 2021 *)

PARI

isok(p) = isprime(p) && ((hammingweight(p) % hammingweight(primepi(p))) == 0); \\ Michel Marcus, Jun 14 2021