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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A214139 A215656 A308889 * A061154 A252690 A134212 Adjacent sequences: A214616 A214617 A214618 * A214620 A214621 A214622 KEYWORD nonn,base AUTHOR Alex Ratushnyak, Jul 23 2012 STATUS approved

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Last modified November 27 19:48 EST 2022. Contains 358406 sequences. (Running on oeis4.)