A095286 - OEIS

%I #22 Jun 05 2020 04:05:44

%S 3,7,11,13,23,29,31,43,47,53,59,61,79,103,107,109,127,151,157,167,173,

%T 179,181,191,199,211,223,227,229,233,239,241,251,311,317,347,349,359,

%U 367,373,379,383,431,439,443,461,463,467,479,487,491,499

%N Primes in whose binary expansion the number of 1 bits is > 1 + number of 0 bits.

%H Indranil Ghosh, <a href="/A095286/b095286.txt">Table of n, a(n) for n = 1..25000</a>

%H A. Karttunen and J. Moyer: <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%e 13 is in the sequence because 13 is prime and 13 = 1101_2. '1101' has three 1's and one 0. 3 > 1 + 1. - _Indranil Ghosh_, Feb 07 2017

%o (PARI)B(x) = {nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;

%o for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );

%o if(b1 > (b0+1), return(1);, return(0);); };

%o forprime(x = 3, 499, if(B(x), print1(x, ", "); ); );

%o \\ _Washington Bomfim_, Jan 11 2011

%o (Python)

%o from sympy import isprime

%o i = 1

%o j = 1

%o while j <= 2000:

%o     bi = bin(i)[2:]

%o     if isprime(i) and bi.count("1") > 1 + bi.count("0"):

%o         print(str(j) + " " + str(i))

%o         j += 1

%o     i += 1 # _Indranil Ghosh_, Feb 07 2017

%Y Complement of A095287 in A000040. Subset of A095070. Subset: A095314. Cf. also A095296.

%K nonn,easy,base

%O 1,1

%A _Antti Karttunen_, Jun 04 2004