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

Author

Antti Karttunen, May 14 2015

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Complement among primes: A081092.

Intersection of A000040 and A084345.

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

Cf. A000120.

Programs

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)))))))