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A225222 Primes with more than twice as many 1s as 0s in binary. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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 *)

PROG

(PARI) has(n)=3*hammingweight(n)>2*#binary(n)

select(has, primes(500))

CROSSREFS

Cf. A095070, A095314.

Sequence in context: A310200 A095286 A177681 * A106561 A296929 A111363

Adjacent sequences:  A225219 A225220 A225221 * A225223 A225224 A225225

KEYWORD

nonn,base

AUTHOR

Charles R Greathouse IV, May 02 2013

STATUS

approved

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)