A225222 Primes with more than twice as many 1's as 0's in binary.

3, 7, 11, 13, 23, 29, 31, 47, 59, 61, 79, 103, 107, 109, 127, 191, 223, 239, 251, 367, 379, 383, 431, 439, 443, 463, 479, 487, 491, 499, 503, 509, 607, 631, 701, 719, 727, 733, 743, 751, 757, 761, 823, 827, 829, 859, 863, 877, 883, 887, 911, 919, 941, 947, 953, 967, 971

Offset: 1

Author

Charles R Greathouse IV, May 02 2013

Keywords

• nonn
• base

Comments

Naslund proves that this sequence (and related ones) is infinite and gives an asymptotic upper bound.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Naslund, Bounds for the tail distribution of the sum of digits of prime numbers, arXiv:1211.2455 [math.NT], 2012.
• Eric Naslund, The tail distribution of the sum of digits of prime numbers, Uniform Distribution Theory 10 (2015), no. 1, 63-68. See the abstract and p. 64.

Crossrefs

Cf. A095070, A095314.

Programs

Mathematica

okQ[n_] := Module[{b = IntegerDigits[n, 2]}, Count[b, 1] > 2*Count[b, 0]]; Select[Prime[Range[200]], okQ] (* T. D. Noe, May 02 2013 *)

PARI

has(n)=3*hammingweight(n)>2*#binary(n)
select(has,primes(500))