cp's OEIS Frontend

A330671 Largest number whose base-n expansion cannot be subdivided to form a sequence of numbers which ordered form a multiple of n+1 when using +, *, and ().

%I A330671 #51 May 24 2021 00:08:14
%S A330671 1,7,13,41,206,335,503,2746,9898,13938,20588,28390,38007,50366,
%T A330671 1006418,82650,1865809,1738855,2879137,4024861,5135433,5585431,7932985
%N A330671 Largest number whose base-n expansion cannot be subdivided to form a sequence of numbers which ordered form a multiple of n+1 when using +, *, and ().
%C A330671 Each valid number in a given base n must be a one-digit extension to the right (or left) of another valid number in the same base; otherwise, you could ignore the added digit, make a multiple of n+1 with the rest of the number, then multiply it by the new digit to get a multiple of n+1.
%C A330671 a(n) is always less than n^(n+1).
%C A330671 a(n) also appears to be less than n^(n/2), except at n=3.
%H A330671 Tomas Rigaux, <a href="/A330671/a330671.py.txt">Python generator code</a>
%e A330671 For n = 2, the binary notation of a number cannot contain any 0, as you could then construct 0 by multiplying all the digits together, so the only candidates are 1, 11, 111, 1111 (or 1, 3, 7, 15, ... in base 10).
%e A330671 Out of those, if you have at least 2 digits, the number contains the substring '11', which can be multiplied by all the other digits to give 11 (or 3 in base 10), which gives a(2) = 1 as the largest and only solution.
%e A330671 For n = 4, a(n) = 13 can be easily checked using the fact that the base-4 expansion of a valid number cannot contain a 2 and a 3 next to each other, as 2+3 = 5 = n+1.
%e A330671 For n = 10, 12345 is not a valid number as 1+2*3*4*5 = 121 = 11*11.
%o A330671 (Python) # See Python link
%K A330671 nonn,more,base
%O A330671 2,2
%A A330671 _Tomas Rigaux_, Jan 18 2020