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Numbers n such that A278981(n) < 2*n^2.
4

%I #21 Jan 02 2017 20:03:58

%S 6,8,12,18,20,24,28,30,32,36,40,42,44,48,50,52,54,56,60,64,66,70,72,

%T 80,84,88,90,96,108,112,116,120,126,132,140,144,148,150,156,160,162,

%U 168,174,176,180,186,188,192,196,198,200,204,210,216,220,224,230,232,234,240

%N Numbers n such that A278981(n) < 2*n^2.

%C All members of this sequence are even, as for any odd number m A278981(m) > m^3 + m^2 + m + 1 > 2*m^2.

%C It appears that, apart from 2, all members of A280236 appear in this sequence.

%H Ely Golden, <a href="/A280270/b280270.txt">Table of n, a(n) for n = 1..1889</a>

%H Ely Golden, <a href="/A280270/a280270_1.txt">Table of n, a(n), A278981(a(n)) for n = 1..1889 (a-file)</a>

%o (SageMath)

%o def nonZeroDigits(x, n):

%o if(x<=0|n<2):

%o return []

%o li=[]

%o while(x>0):

%o d=divmod(x, n)

%o if(d[1]!=0):

%o li.append(d[1])

%o x=d[0]

%o li.sort()

%o return li;

%o def nonZeroFactorDigits(x, n):

%o if(x<=0|n<2):

%o return []

%o li=[]

%o f=list(factor(x))

%o #ensures inequality of nonZeroFactorDigits(x, n) and nonZeroDigits(x, n) if x is prime

%o if((len(f)==1)&(f[0][1]==1)):

%o return [];

%o for c in range(len(f)):

%o for d in range(f[c][1]):

%o ld=nonZeroDigits(f[c][0], n)

%o li+=ld

%o li.sort()

%o return li;

%o #the actual function

%o def a(n):

%o c=n**2+n+1

%o limit=2*(n**2)

%o if(n%2!=0):

%o return -1

%o while((nonZeroFactorDigits(c, n)!=nonZeroDigits(c, n))&(c<limit)):

%o c+=1;

%o if(c>=limit):

%o return -1

%o return c;

%o index=1

%o value=2

%o while(index<=1000):

%o result=a(value)

%o if(result!=-1):

%o print(str(index)+" "+str(value)+" "+str(result))

%o index+=1

%o value+=1

%o print("complete")

%Y Cf. A278981, A280236.

%K nonn,base

%O 1,1

%A _Ely Golden_, Dec 30 2016