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A280270
Numbers n such that A278981(n) < 2*n^2.
4
6, 8, 12, 18, 20, 24, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 70, 72, 80, 84, 88, 90, 96, 108, 112, 116, 120, 126, 132, 140, 144, 148, 150, 156, 160, 162, 168, 174, 176, 180, 186, 188, 192, 196, 198, 200, 204, 210, 216, 220, 224, 230, 232, 234, 240
OFFSET
1,1
COMMENTS
All members of this sequence are even, as for any odd number m A278981(m) > m^3 + m^2 + m + 1 > 2*m^2.
It appears that, apart from 2, all members of A280236 appear in this sequence.
PROG
(SageMath)
def nonZeroDigits(x, n):
if(x<=0|n<2):
return []
li=[]
while(x>0):
d=divmod(x, n)
if(d[1]!=0):
li.append(d[1])
x=d[0]
li.sort()
return li;
def nonZeroFactorDigits(x, n):
if(x<=0|n<2):
return []
li=[]
f=list(factor(x))
#ensures inequality of nonZeroFactorDigits(x, n) and nonZeroDigits(x, n) if x is prime
if((len(f)==1)&(f[0][1]==1)):
return [];
for c in range(len(f)):
for d in range(f[c][1]):
ld=nonZeroDigits(f[c][0], n)
li+=ld
li.sort()
return li;
#the actual function
def a(n):
c=n**2+n+1
limit=2*(n**2)
if(n%2!=0):
return -1
while((nonZeroFactorDigits(c, n)!=nonZeroDigits(c, n))&(c<limit)):
c+=1;
if(c>=limit):
return -1
return c;
index=1
value=2
while(index<=1000):
result=a(value)
if(result!=-1):
print(str(index)+" "+str(value)+" "+str(result))
index+=1
value+=1
print("complete")
CROSSREFS
Sequence in context: A372011 A090259 A089241 * A368242 A315862 A315863
KEYWORD
nonn,base
AUTHOR
Ely Golden, Dec 30 2016
STATUS
approved