A214619 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.

148, 162, 180, 216, 264, 270, 296, 324, 432, 450, 462, 486, 540, 648, 720, 810, 814, 864, 962, 1035, 1056, 1072, 1080, 1089, 1107, 1125, 1215, 1224, 1248, 1250, 1260, 1269, 1296, 1320, 1326, 1359, 1386, 1395, 1426, 1443, 1450, 1458, 1480, 1482, 1485, 1488, 1515

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..47.

Example

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

Prog

(Python)
# primes = [...]
TOP = 10000
smallest = [0]*TOP
largest  = [0]*TOP
digitset = [0]*TOP
flags = [0]*TOP
for n in range(1, TOP):
    curSm = curLa = curDi = 0
    t = x = n
    while x:
        curDi += 10**( x%10 )
        x /= 10
    for p in primes:
        if t%p==0:
            if curSm==0:
                curSm = p
            curLa = p
            t/=p
            while t%p==0:
                t/=p
            if t==1:
                break
    digitset[n] = curDi
    smallest[n] = curSm
    largest[n]  = curLa
    for k in range(1, n):
        if smallest[k]==curSm and largest[k]==curLa and digitset[k]==curDi:
            flags[k]+=1
            flags[n]+=1
for n in range(1, TOP):
    if flags[n]>0:
        print n,

Crossrefs

Cf. A214620, A214621.

Sequence in context: A215656 A367738 A308889 * A061154 A252690 A134212

Adjacent sequences: A214616 A214617 A214618 * A214620 A214621 A214622

Keyword

nonn,base

Author

Alex Ratushnyak, Jul 23 2012

Status

approved