A370361 Minimum greatest prime factor for a length n number with 2 distinct digits, excluding multiples of 10.

2, 3, 3, 7, 11, 29, 19, 19, 23, 67, 29, 139, 107, 71, 101, 137, 127, 307, 173, 347, 383, 439, 271, 853, 521, 587, 883, 571, 823, 941

Offset: 2

Author

Ed Pegg Jr, Mar 05 2024

Keywords

• nonn
• hard
• more
• base

Comments

Multiples of ten are disallowed, because that would give A010716 (all 5) preceded by 2, 3, 3.

Corresponds to 2-distinct-digit numbers in A370849, except at a(21) where 101010110010001010011 with zero digits is more smooth than 222229999999292992929.

Examples

			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
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
		

Links

• Lucas A. Brown, Python program.

Crossrefs

Cf. A006530, A370849.

Programs

Python

from sympy import primefactors
from sympy.utilities.iterables import multiset_permutations
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

Python

# See LINKS. Lucas A. Brown, Mar 30 2024

Formula

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

Extensions

a(21)-a(23) from Michael S. Branicky, Mar 05 2024

a(24)-a(25) from David A. Corneth, Mar 05 2024

a(26)-a(30) from Don Reble, Mar 06 2024

a(31) from Lucas A. Brown, Mar 30 2024