I got confused too. I looked at A209674, which has the description -------- For each n >= 1, define a sequence S(n) by S(0)=n, S(i) = sum of last two digits of (S(0), S(1), ..., S(n-1)); a(n) = smallest m such that S(m) = 5, or -1 if 5 is never reached. -------- So at first glance it SEEMS that you're to sum the last two digits of ALL the previous S(n). However the example for S4 is given as S4(0) = 4 S4(1) = 4 S4(2) = 8 S4(3) = 12 S4(4) = 3 S4(5) = 5 But if you summed everything then S4(3) would be 16 instead. What I think is actually going on is more like you append digits onto a string, and then sum the last two and append them, and so on 4 44 448 44812 448123 4481235. S1 would then apparently go 1 11 112 1123 11235. Which checks So S321 would go 321 3213 32134 321347 32134711 321347112 3213471123 32134711235. Giving a(321)=7. I would suggest that the description would be a lot clearer if A. a better notation than (S(0), S(1), ..., S(n-1)) was used for string concatenation, perhaps S(0):S(1):...:S(n-1) B. the index variable n wasn't reused to mean two different things, perhaps by writing Sn(k) for the k-th element of the auxiliary digit string sequence used to compute a(n).
="Schroeppel, Richard" <rschroe@sandia.gov>
Could you sketch a bit more of what's going on here? Suppose S begins with 321. How does this hit 5?
Rich
________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] on behalf of Eric Angelini [Eric.Angelini@kntv.be] Sent: Sunday, March 11, 2012 12:23 PM To: math-fun Subject: [EXTERNAL] [math-fun] Hitting 5
Start sequence S with any integer. If a(n) is the sum of the last two digits of S, S will always hit 5 at some point. Best, É.
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