A361071 Let c1(p) be the number of primes <= p with an odd number of 1's in base 2, and let c2(p) be the number of primes <= p with an even number of 1's in base 2. a(n) is the least prime p such that abs(c1(p) - c2(p)) >= n.

2, 13, 41, 61, 67, 79, 109, 131, 137, 173, 179, 181, 191, 193, 211, 223, 227, 229, 233, 239, 241, 251, 587, 613, 617, 641, 653, 659, 661, 719, 727, 733, 761, 769, 829, 953, 967, 971, 1009, 1021, 1039, 1069, 1087, 1193, 1201, 1213, 1697, 1721, 1753, 1759, 1777, 1783, 1787

Offset: 1

Author

Jean-Marc Rebert, Mar 01 2023

Keywords

• nonn
• base

Examples

			a(1) = 2, because c1(2) = 1 and c2(2) = 0, so abs(c1(2) - c2(2)) = 1 >= 1, and no lesser prime satisfies this.
		

Crossrefs

Cf. A130911, A027697, A027699.

Programs

PARI

{ r = 0; n = 1; forprime (p = 2, 1787, r += (-1)^hammingweight(p); if (n==abs(r), print1 (p", "); n++;);); } \\ Rémy Sigrist, Mar 01 2023