A280971 Composite numbers having the same bits as their prime factors (with multiplicity), including zero bits.

159, 287, 303, 319, 591, 623, 679, 687, 699, 763, 1135, 1167, 1203, 1243, 1247, 1271, 1351, 1371, 1391, 1631, 2167, 2173, 2231, 2285, 2319, 2359, 2463, 2471, 2495, 2519, 2743, 2779, 2787, 2809, 2863, 2931, 2933, 2991, 3029, 3039, 3503, 4223, 4279, 4287, 4319, 4343, 4411, 4439, 4479, 4487

Offset

1,1

Comments

Binary equivalent of A280928.

Subsequence of A278909 as well as A280967. The terms in A278909 and A280967 but not this sequence are given by A280972.

Links

Ely Golden, Table of n, a(n) for n = 1..10000

Prog

(SageMath)
def factorbits(x):
    if(x<2):
        return (0, 0);
    s=0; t=0
    f=list(factor(x));
    #ensures inequality of numfactorbits(x) and bin(x).count("1") if x is prime
    if((len(f)==1)&(f[0][1]==1)):
        return (0, 0);
    for c in range(len(f)):
        s+=bin(f[c][0]).count("1")*f[c][1]
        t+=(bin(f[c][0]).count("0")-1)*f[c][1]
    return (s, t);
counter=2
index=1
while(index<=10000):
    if(factorbits(counter)==(bin(counter).count("1"), bin(counter).count("0")-1)):
        print(str(index)+" "+str(counter))
        index+=1;
    counter+=1;

Crossrefs

Cf. A278909, A280967, A280928.

Sequence in context: A281665 A329535 A250659 * A090948 A242115 A227709

Adjacent sequences: A280968 A280969 A280970 * A280972 A280973 A280974

Keyword

nonn,base

Author

Ely Golden, Jan 11 2017

Status

approved