A266001 - OEIS

%I #23 Feb 13 2016 23:02:30

%S 1,2,5,7,13,14,22,23,25,26,41,43,53,121,122,125,149,151,157,158,214,

%T 215,229,230,233,238,239,365,367,373,374,377,445,446,473,475,485,607,

%U 617,619,634,635,637,638,697,698,701,725,727,1366,1367,1373,1375,1429,1430,1445,1447,1453,1454

%N Numbers with no 0's in their base 3 and base 4 expansions.

%C Intersection of A023705 and A032924.

%C 1, 7 and 32767 also share this property in base 2.

%H Chai Wah Wu, <a href="/A266001/b266001.txt">Table of n, a(n) for n = 1..12682</a>

%e 53 is 1222 in base 3 and 311 in base 4; no zeros are shown in either representation and so 53 is a term.

%e Similarly, 121 is 11111 in base 3 and 1321 in base 4 so it is also a term.

%o (PARI) isokd(n) = vecmin(digits(n, 3)) && vecmin(digits(n, 4)); \\ _Michel Marcus_, Jan 28 2016

%o (Python)

%o from __future__ import division

%o from gmpy2 import digits

%o A266001_list = [j for j in (int(format(i,'b'),3)+(3**n-1)//2 for n in range(1,10) for i in range(2**n)) if '0' not in digits(j,4)] # _Chai Wah Wu_, Feb 13 2016

%Y Cf. A023705, A032924, A262958, A262963.

%K nonn,base

%O 1,2

%A _Robin Powell_, Jan 27 2016