[math-fun] A+B=C. Concatenate ABC
Hello Math-Fun, take 3 integers A, B and C such that A+B=C. Concatenate ABC and call the result D. Ds seq is: http://www.research.att.com/~njas/sequences/A108203 Among those Ds some can drive us back to the original A and B: D=123 --> A=1 and B=2 What about D's (D-primes) giving two possible pre- decessors: D'=22830 --> A=2 and B=28 or A=22 and B=8 Are those D's in finite quantity? Best, É.
On Monday 10 March 2008, Eric Angelini wrote:
What about D's (D-primes) giving two possible pre- decessors:
D'=22830 --> A=2 and B=28 or A=22 and B=8
I haven't thought about the actual problem at all, but I suggest that "D-prime" is just about the worst possible name for something whose defining characteristic is having multiple decompositions into simpler parts :-). -- g
On Mon, Mar 10, 2008 at 6:33 AM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun, take 3 integers A, B and C such that A+B=C. Concatenate ABC and call the result D. Ds seq is: http://www.research.att.com/~njas/sequences/A108203<http://www.research.att.com/%7Enjas/sequences/A108203>
Among those Ds some can drive us back to the original A and B:
D=123 --> A=1 and B=2
What about D's (D-primes) giving two possible pre- decessors:
D'=22830 --> A=2 and B=28 or A=22 and B=8
Are those D's in finite quantity?
Best, É.
Suppose a and b are digits such that a+b<10. Then the two pairs A = a.....a (n a's), B=b and A = a B = a.....ab (n-1 a's) generate the same C and are the same when concatenated together. This leads to an infinite family of D-primes. Dave
[Dave]:
Suppose a and b are digits such that a+b<10. Then the two pairs
A = a.....a (n a's), B=b and A = a B = a.....ab (n-1 a's) generate the same C and are the same when concatenated together. This leads to an infinite family of D-primes. ----- ... Indeed, thanks Dave, well done! Best, E.
participants (3)
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Dave Blackston -
Eric Angelini -
Gareth McCaughan