A084345 Numbers with a nonprime number of 1's in their binary expansion (complement of A052294).

0, 1, 2, 4, 8, 15, 16, 23, 27, 29, 30, 32, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60, 63, 64, 71, 75, 77, 78, 83, 85, 86, 89, 90, 92, 95, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 128, 135, 139, 141, 142, 147, 149, 150, 153, 154, 156, 159, 163

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

15 is in the sequence because 15_10=1111_2 and 1+1+1+1=4 is composite.

Mathematica

Select[Range[200], !PrimeQ[DigitCount[#, 2, 1]]&] (* Harvey P. Dale, Jan 21 2013 *)

Prog

(PARI) for(n=0, 200, b=binary(n); if(!isprime(sum(m=1, matsize(b)[2], b[m])), print1(n, ", ")))
(Haskell)
a084345 n = a084345_list !! (n-1)
a084345_list = filter ((== 0) . a010051' . a000120) [0..]
-- Reinhard Zumkeller, Aug 28 2013, Nov 16 2012
(Python)
from math import comb
from sympy import isprime, primerange
def A084345(n):
    def f(x):
        s = bin(x)[-1:1:-1]
        m = x.bit_count()
        l = x.bit_length()
        c = n-1+isprime(m)
        for i in range(l):
            j = int(s[i])
            if j:
                m -= 1
                for p in primerange(m, l+1):
                    c += comb(i, p-m)
        return c
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jun 08 2026

Crossrefs

Cf. A052294.

Cf. A010051, A000120.

Sequence in context: A019278 A267894 A384500 * A084561 A277166 A078613

Adjacent sequences: A084342 A084343 A084344 * A084346 A084347 A084348

Keyword

easy,nonn,base,changed

Author

Zak Seidov, Jun 22 2003

Extensions

More terms from Rick L. Shepherd, Jun 23 2003

Term 0 added by Michel Marcus, Aug 26 2013

b-file adjusted by Reinhard Zumkeller, Aug 28 2013

Status

approved