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A280827 a(n) = A076649(n) - A055642(n). 3
-1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 0, 3, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 4, 1, 2, 0, 2, 1, 1, 0, 3, 0, 1, 1, 2, 1, 2, 0, 3, 2, 1, 0, 2, 1, 1, 1, 3, 0, 2, 1, 2, 1, 1, 1, 4, 0, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

a(1) is the only negative term in this sequence. - Ely Golden, Jan 10 2017

a(n) = 0 if and only if n is a member of A109608. - Ely Golden, Jan 10 2017

LINKS

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

Ely Golden, Proof that a(n)>=0 for all n>1

EXAMPLE

a(10) = 0, as 2*5 have 2 digits total, and 10 has 2 digits. Thus a(10) = 2-2 = 0.

a(1) is defined to be -1, as the empty product has 0 digits, and 1 has 1 digit. Thus a(1) = 0-1 = -1.

PROG

(SageMath)

def digits(x, n):

    if(x<=0|n<2):

        return []

    li=[]

    while(x>0):

        d=divmod(x, n)

        li.insert(0, d[1])

        x=d[0]

    return li;

def factorDigits(x, n):

    if(x<=0|n<2):

        return []

    li=[]

    f=list(factor(x))

    for c in range(len(f)):

        for d in range(f[c][1]):

            ld=digits(f[c][0], n)

            li+=ld

    return li;

def digitDiff(x, n):

    return len(factorDigits(x, n))-len(digits(x, n))

radix=10

index=1

while(index<=10000):

    print(str(index)+" "+str(digitDiff(index, radix)))

    index+=1

CROSSREFS

Cf. A109608, A076649.

Sequence in context: A186714 A160382 A081221 * A103840 A066301 A046660

Adjacent sequences:  A280824 A280825 A280826 * A280828 A280829 A280830

KEYWORD

sign,base,easy

AUTHOR

Ely Golden, Jan 08 2017

STATUS

approved

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Last modified January 19 14:53 EST 2020. Contains 331049 sequences. (Running on oeis4.)