A144214 Primes with both a prime number of 0's and a prime number of 1's in their binary representations.
17, 19, 37, 41, 79, 103, 107, 109, 131, 137, 151, 157, 167, 173, 179, 181, 193, 199, 211, 227, 229, 233, 241, 257, 367, 379, 431, 439, 443, 463, 487, 491, 499, 521, 541, 557, 563, 569, 577, 587, 601, 607, 613, 617, 631, 641, 647, 653, 659, 661, 677, 701, 709
Offset: 1
Examples
79, a prime, in binary is 1001111. This has two 0's and has five 1's. Since both two and five are primes, 79 is included in the sequence.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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Maple
A080791 := proc(n) local i,dgs ; dgs := convert(n,base,2) ; nops(dgs)-add(i,i=dgs) ; end: A000120 := proc(n) local i,dgs ; dgs := convert(n,base,2) ; add(i,i=dgs) ; end: isA144214 := proc(n) local no0,no1 ; no0 := A080791(n) ; no1 := A000120(n) ; isprime(n) and isprime(no0) and isprime(no1) ; end: for n from 1 to 1200 do if isA144214(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 17 2008
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Mathematica
Select[Prime[Range[6! ]],PrimeQ[DigitCount[ #,2,0]]&&PrimeQ[DigitCount[ #,2,1]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)
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Python
from sympy import isprime def ok(n): return isprime(c:=n.bit_count()) and isprime(n.bit_length()-c) and isprime(n) print([k for k in range(710) if ok(k)]) # Michael S. Branicky, Dec 27 2023
Extensions
More terms from R. J. Mathar, Sep 17 2008