A280270 Numbers n such that A278981(n) < 2*n^2.

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

Author

Ely Golden, Dec 30 2016

Keywords

• nonn
• base

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.

Links

• Ely Golden, Table of n, a(n) for n = 1..1889
• Ely Golden, Table of n, a(n), A278981(a(n)) for n = 1..1889 (a-file)

Crossrefs

Cf. A278981, A280236.

Programs

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):
        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")