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A225222
Primes with more than twice as many 1's as 0's 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
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
Sequence in context: A310200 A095286 A177681 * A106561 A296929 A111363
KEYWORD
nonn,base
AUTHOR
STATUS
approved