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Primes in whose binary expansion the number of 1-bits is one more than the number of 0-bits.
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%I #22 May 01 2021 15:57:41

%S 5,19,71,83,89,101,113,271,283,307,313,331,397,409,419,421,433,457,

%T 1103,1117,1181,1223,1229,1237,1303,1307,1319,1381,1427,1429,1433,

%U 1481,1489,1559,1579,1607,1613,1619,1621,1637,1699,1733,1811,1861

%N Primes in whose binary expansion the number of 1-bits is one more than the number of 0-bits.

%H Indranil Ghosh, <a href="/A095073/b095073.txt">Table of n, a(n) for n = 1..25000</a>

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

%e 71 is in the sequence because 71_10 = 1000111_2. '1000111' has four 1's and three 0's. - _Indranil Ghosh_, Feb 03 2017

%t Select[Prime[Range[500]], Differences[DigitCount[#, 2]] == {-1} &]

%o (PARI)

%o { forprime(p=2, 2000,

%o v=binary(p); s=0;

%o for(k=1,#v, s+=if(v[k]==1,+1,-1));

%o if(s==1,print1(p,", "))

%o ) }

%o (Python)

%o from sympy import isprime

%o i=1

%o j=1

%o while j<=25000:

%o if isprime(i) and bin(i)[2:].count("1")-bin(i)[2:].count("0")==1:

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

%o j+=1

%o i+=1 # _Indranil Ghosh_, Feb 03 2017

%Y Intersection of A000040 and A031448. Subset of A095070. Cf. A095053.

%K nonn,base,easy

%O 1,1

%A _Antti Karttunen_, Jun 01 2004