[seqfan] No 10-sum in any chunk of digits

Eric Angelini Eric.Angelini at kntv.be
Sun Nov 17 00:13:53 CET 2013

Hello SeqFans,
We want a seq S where it is impossible to
reach exactly 10 by summing any sub-
chain of consecutive digits in S.

S is strictly increasing here:

S = 1,2,3,6,7,8,9,20,21,22,25,26,30,31,40,43,44,45,47,48,49,50,60,61,62,63,65,66,67,68,69,70,71,74,75,76,77,78,...

We see that S cannot start with:
S = 1,2,3,4,... as 1+2+3+4 = 10

neither with:
S = 1,2,3,5,... as 2+3+5 = 10

Thus S starts with:
S = 1,2,3,6,... as no sub-chain of digits
sums up to 10 yet.

To extend S we always take the 
smallest integer bigger than the
previous one and not leading to a
T follows the same rule but is 
extended with the smallest integer 
not yet present in T and not leading 
to a contradiction:

T = 1,2,3,6,5,4,7,8,9,20,10,11,12,18,30,13,14,31,34,16,15,17,18,32,21,33,23,35,36,24,25,22,27,26,36,29,38,39,40,...

T is not a permutation of the naturals 
without the integers listed in A052224 
("Numbers whose sum of digits is 10") 
as 11111111, for instance, with its 8 digits "1", 
cannot be part of T.
Why did we consider the 10-sum constraint?
Because if we forbid any chunk of 
digits of sum 9, for instance, we must 
forbid all 9s in T as a single digit "9" 
is a chunk of size one (well, why not 
have a try, after all?)

We could also build respectively an S'
and a T' seq with an 11-sum interdiction (or a 12-sum interdiction -- or a 666-sum ban)...


Catapulté de mon aPhone

More information about the SeqFan mailing list