%I #71 Mar 31 2024 12:02:24
%S 2,3,3,7,11,29,19,19,23,67,29,139,107,71,101,137,127,307,173,347,383,
%T 439,271,853,521,587,883,571,823,941
%N Minimum greatest prime factor for a length n number with 2 distinct digits, excluding multiples of 10.
%C Multiples of ten are disallowed, because that would give A010716 (all 5) preceded by 2, 3, 3.
%C Corresponds to 2-distinct-digit numbers in A370849, except at a(21) where 101010110010001010011 with zero digits is more smooth than 222229999999292992929.
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A370361.py">Python program</a>.
%F a(n) = A006530(A370849(n)) unless the smoothest solution is (as for n = 21) a number made of digits {0, 1}, currently excluded in A370849. - _M. F. Hasler_, Mar 05 2024
%e a(7) = 29 as the largest prime factor of the 7-digit number with exactly two distinct digits, 1111222, is 29 and no 7-digit number with exactly two distinct digits has a smaller largest prime factor and no 7-digit number with exactly two distinct digits smaller than 1111222 has a largest prime factor that is equal to 29. - _David A. Corneth_, Mar 05 2024
%e a(9) = 19, because 799779977 = 17*19^6 has nine digits, two distinct digits and largest prime factor 19. - _Ed Pegg Jr_, Mar 05 2024
%o (Python)
%o from sympy import primefactors
%o from sympy.utilities.iterables import multiset_permutations
%o def A370361(n): return min((max(primefactors(a:=int(''.join(s)))),a) for i in range(10) for j in range(i+1,10) for k in range(1,n) for s in multiset_permutations(str(i)*k+str(j)*(n-k)) if s[0] != '0' and s[-1] != '0')[0] # _Chai Wah Wu_, Mar 09 2024
%o (Python) # See LINKS. _Lucas A. Brown_, Mar 30 2024
%Y Cf. A006530, A370849.
%K nonn,hard,more,base
%O 2,1
%A _Ed Pegg Jr_, Mar 05 2024
%E a(21)-a(23) from _Michael S. Branicky_, Mar 05 2024
%E a(24)-a(25) from _David A. Corneth_, Mar 05 2024
%E a(26)-a(30) from _Don Reble_, Mar 06 2024
%E a(31) from _Lucas A. Brown_, Mar 30 2024