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A095073 Primes in whose binary expansion the number of 1-bits is one more than the number of 0-bits. 6
5, 19, 71, 83, 89, 101, 113, 271, 283, 307, 313, 331, 397, 409, 419, 421, 433, 457, 1103, 1117, 1181, 1223, 1229, 1237, 1303, 1307, 1319, 1381, 1427, 1429, 1433, 1481, 1489, 1559, 1579, 1607, 1613, 1619, 1621, 1637, 1699, 1733, 1811, 1861 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
71 is in the sequence because 71_10 = 1000111_2. '1000111' has four 1's and three 0's. - Indranil Ghosh, Feb 03 2017
MATHEMATICA
Select[Prime[Range[500]], Differences[DigitCount[#, 2]] == {-1} &]
PROG
(PARI)
{ forprime(p=2, 2000,
v=binary(p); s=0;
for(k=1, #v, s+=if(v[k]==1, +1, -1));
if(s==1, print1(p, ", "))
) }
(Python)
from sympy import isprime
i=1
j=1
while j<=25000:
if isprime(i) and bin(i)[2:].count("1")-bin(i)[2:].count("0")==1:
print(str(j)+" "+str(i))
j+=1
i+=1 # Indranil Ghosh, Feb 03 2017
CROSSREFS
Intersection of A000040 and A031448. Subset of A095070. Cf. A095053.
Sequence in context: A026590 A243413 A222538 * A128349 A255449 A296630
KEYWORD
nonn,base,easy
AUTHOR
Antti Karttunen, Jun 01 2004
STATUS
approved

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Last modified July 12 17:26 EDT 2024. Contains 374251 sequences. (Running on oeis4.)