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%I #12 Feb 22 2024 19:33:24
%S 1010100,2200100,20130000,3243003420,55111253530,5411665056000,
%T 33254100107730,210324811482600,977731833235239280
%N Smallest composite integer in base n which remains composite after altering any one or two digits.
%C 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.
%H Witold Jarnicki and Maciej Zenczykowski, <a href="http://arXiv.org/abs/0709.3361">On a property of the number 977731833235239280</a>, arXiv:0709.3361 [math.NT], 2007
%e 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.
%Y Cf. A220289.
%K base,more,nonn
%O 2,1
%A _Jonathan Vos Post_, Oct 11 2007
%E a(2) and the definition were corrected by Witold Jarnicki, Oct 11 2007