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 A062406 Cardinality of the (ordered) list L_n defined inductively by: L_1 = {2}; L_(n+1) = L_n - {p}, where p is the first member of L_n, from left to right, such that prime(n+1) can be appended to the end or beginning of p so that the neighboring digits are equal, if p exists; append prime(n+1) to the end of L_n, otherwise. 2
 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 5, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 12, 13, 14, 13, 14, 15, 16, 17, 18, 17, 16, 17, 18, 19, 18, 19, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 11, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that a(n) is growing slowly on the average. (A moving average filter applied to the sequence will show an upward trend.) Probably a(n) > 0 for all n, but lacking a proof, one is never sure. For example, L_9 = {5} comes perilously close to extinction. It would be interesting to have a closed-form expression giving, at least asymptotically, the value of a(n). LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..10000 EXAMPLE L_n for n = 1..5 are: {2}, {2,3}, {2,3,5}, {2,3,5,7}, {2,3,5,7,11}. The first five values of the sequence are then 1,2,3,4,5, respectively. For n = 6, Prime(6) = 13 can be appended to the beginning of 3 in L_5 so that the neighboring digits (i.e., 3's) are equal, so eliminate 3 from L_5 to get L_6 = {2,5,7,11}. Hence a(6) = 4. PROG (Sage) def a_list(n) : res = [] curlist = [] for m in range(1, n+1) : d = nth_prime(m).digits() ds = (d[-1], d[0]) remitem = next((i for i in range(len(curlist)) if curlist[i][0] == ds[1] or curlist[i][1] == ds[0]), None) if remitem != None : del curlist[remitem] else : curlist.append(ds) res.append(len(curlist)) return res # Eric M. Schmidt, Oct 19 2016 CROSSREFS Cf. A067854. Sequence in context: A086144 A131974 A181975 * A271800 A073792 A017870 Adjacent sequences: A062403 A062404 A062405 * A062407 A062408 A062409 KEYWORD nonn,base AUTHOR Joseph L. Pe, Feb 13 2002 EXTENSIONS Extended and corrected and definition edited by Eric M. Schmidt, Oct 19 2016 STATUS approved

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Last modified December 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)