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

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

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.

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

Mathematica

Select[Prime[Range[6! ]], PrimeQ[DigitCount[ #, 2, 0]]&&PrimeQ[DigitCount[ #, 2, 1]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)

Prog

(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

Crossrefs

Cf. A081092, A144213, A178350.

Sequence in context: A144213 A318940 A289355 * A191043 A306510 A129805

Adjacent sequences: A144211 A144212 A144213 * A144215 A144216 A144217

Keyword

base,nonn

Author

Leroy Quet, Sep 14 2008

Extensions

More terms from R. J. Mathar, Sep 17 2008

Status

approved