A133219 Smallest composite integer in base n which remains composite after altering any one or two digits.

1010100, 2200100, 20130000, 3243003420, 55111253530, 5411665056000, 33254100107730, 210324811482600, 977731833235239280

Offset: 2

Author

Jonathan Vos Post, Oct 11 2007

Keywords

• base
• more
• nonn

Comments

Changing the most significant digit to 0 is allowed. The problem (base 10) was posed by W. Sierpinski, published in 1977. There are an infinite number of solutions if a certain Erdos conjecture on congruences is true. a(2) through a(9) are proved minimal, a(10) has not yet been proved minimal.

Examples

			a(3) base 10 = 1953. a(4) base 10 = 34560. a(5) base 10 = 7000485. a(6) base 10 = 354748446. a(7) base 10 = 77478704205. a(8) base 10 = 1878528135128. a(9) base 10 = 48398467146642.
		

Links

• Witold Jarnicki and Maciej Zenczykowski, On a property of the number 977731833235239280, arXiv:0709.3361 [math.NT], 2007

Crossrefs

Cf. A220289.

Extensions

a(2) and the definition were corrected by Witold Jarnicki, Oct 11 2007