A072439 Primes prime(k) such that the number of binary 1's in prime(k) equals the number of binary 1's in k.

2, 5, 41, 67, 73, 83, 97, 113, 193, 197, 211, 269, 281, 283, 353, 389, 521, 523, 547, 563, 587, 593, 601, 647, 661, 691, 929, 937, 1061, 1063, 1097, 1109, 1117, 1123, 1289, 1319, 1361, 1381, 1489, 1549, 1559, 1567, 1571, 1579, 1597, 1801, 1873, 2069

Offset: 1

Author

Reinhard Zumkeller, Jun 17 2002

Keywords

• nonn
• base

Examples

			In binary representation 13 and A000040(13)=41 have three 1's: 13='1101' and 41='101001', therefore 41 is a term.
		

Links

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

Crossrefs

Cf. A000040, A000120, A014499, A033548, A049084, A071600, A090455.

Programs

Mathematica

Prime[Select[Range[400], DigitCount[#, 2, 1] == DigitCount[Prime[#], 2, 1] &]] (* Amiram Eldar, Aug 03 2023 *)

PARI

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

Formula

A000120(a(n)) = A000120(A071600(n)) = A014499(n).

A090455(A049084(a(n))) = 0.

a(n) = A000040(A071600(n)).