A072439 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

FORMULA

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

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

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A004096 A156152 A106885 * A286560 A002592 A054553

Adjacent sequences: A072436 A072437 A072438 * A072440 A072441 A072442

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Jun 17 2002

STATUS

approved