A376235 Prime numbers with Hamming weight neither prime nor a power of 2.

311, 317, 347, 349, 359, 373, 461, 467, 571, 599, 619, 683, 691, 739, 797, 811, 821, 839, 853, 857, 881, 907, 937, 977, 991, 1019, 1021, 1103, 1117, 1181, 1223, 1229, 1237, 1279, 1303, 1307, 1319, 1381, 1427, 1429, 1433, 1471, 1481, 1489, 1531, 1559, 1579, 1607, 1613, 1619, 1621, 1637, 1663

Offset: 1

Author

M. F. Hasler, Oct 24 2024

Keywords

• nonn

Comments

Surprisingly, all primes less than 311 have a Hamming weight (sum of their binary digits: A000120) equal to either a prime or a power of two (cf. A174090). But for larger primes, exceptions become more and more frequent.

Crossrefs

Cf. A000120 (binary or Hamming weight), A174090 (union of primes and powers of two).

Programs

PARI

select( {is_A376235(n)=!is_A174090(hammingweight(n))&&isprime(n)}, [0..2222])