A214619 - OEIS

%I #10 Aug 02 2012 16:59:39

%S 148,162,180,216,264,270,296,324,432,450,462,486,540,648,720,810,814,

%T 864,962,1035,1056,1072,1080,1089,1107,1125,1215,1224,1248,1250,1260,

%U 1269,1296,1320,1326,1359,1386,1395,1426,1443,1450,1458,1480,1482,1485,1488,1515

%N Numbers n such that at least one other integer m exists with the same smallest prime factor, same largest prime factor, and same set of decimal digits as n.

%C Decimal digits of m are a permutation of decimal digits of n.

%C Conjecture: there is an X such that among integers bigger than X more than 50% are in the sequence.

%e 148 and 814 have the same set of decimal digits, same smallest prime factor 2, and same largest prime factor 37, so both 148 and 814 are in the sequence.

%e 1080 and 1800 have the same set of decimal digits, same smallest prime factor 2, and same largest prime factor 5.

%o (Python)

%o # primes = [...]

%o TOP = 10000

%o smallest = [0]*TOP

%o largest  = [0]*TOP

%o digitset = [0]*TOP

%o flags = [0]*TOP

%o for n in range(1,TOP):

%o     curSm = curLa = curDi = 0

%o     t = x = n

%o     while x:

%o         curDi += 10**( x%10 )

%o         x /= 10

%o     for p in primes:

%o         if t%p==0:

%o             if curSm==0:

%o                 curSm = p

%o             curLa = p

%o             t/=p

%o             while t%p==0:

%o                 t/=p

%o             if t==1:

%o                 break

%o     digitset[n] = curDi

%o     smallest[n] = curSm

%o     largest[n]  = curLa

%o     for k in range(1,n):

%o         if smallest[k]==curSm and largest[k]==curLa and digitset[k]==curDi:

%o             flags[k]+=1

%o             flags[n]+=1

%o for n in range(1,TOP):

%o     if flags[n]>0:

%o         print n,

%Y Cf. A214620, A214621.

%K nonn,base

%O 1,1

%A _Alex Ratushnyak_, Jul 23 2012