A255564 Primes having in binary representation a nonprime number of 1's.

2, 23, 29, 43, 53, 71, 83, 89, 101, 113, 139, 149, 163, 197, 263, 269, 277, 281, 293, 311, 317, 337, 347, 349, 353, 359, 373, 383, 389, 401, 449, 461, 467, 479, 503, 509, 523, 547, 571, 593, 599, 619, 643, 673, 683, 691, 739, 751, 773, 797, 811, 821, 839, 853, 857, 863, 881, 887, 907, 937, 977, 983, 991, 1013, 1019, 1021, 1031, 1049, 1061

Offset

1,1

Comments

Equally: 2 followed by all primes with their hamming weight a composite number.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

2, which in binary (A007088) is "10", has just one 1-bit, and 1 is not a prime, thus 2 is included in the sequence.
23, which in binary is "10111", has four 1-bits, and 4 is not a prime, thus 23 is included in the sequence.

Prog

(PARI)
i = 0; forprime(n=2, 2^31, if(!isprime(hammingweight(n)), i++; write("b255564.txt", i, " ", n); if(i>=10000, return(n))));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A255564 (MATCHING-POS 1 1 (lambda (n) (and (prime? n) (not (prime? (A000120 n)))))))

Crossrefs

Complement among primes: A081092.

Intersection of A000040 and A084345.

Subsequences: A027699 \ A019434, A085448, A095077, A255569.

Cf. A000120.

Sequence in context: A114549 A235148 A208325 * A034843 A084373 A107148

Adjacent sequences: A255561 A255562 A255563 * A255565 A255566 A255567

Keyword

nonn

Author

Antti Karttunen, May 14 2015

Status

approved