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 A293838 "Look once to the left" sequence starting with 1,2 (see comment). 1
 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Stage 0: we start from 1,2. Stage 1: we add one copy of the block to the left of the last term (here the block 1) giving 1,2,1. Stage 2: we add one copy of the block to the left of the last term (here the block 1,2) giving 1,2,1,1,2. Stage 3: we add one copy of the block to the left of the last term (here the block 1,2,1,1) giving 1,2,1,1,2,1,2,1,1. Iterate the process. At stage n there are 2^n+1 terms. LINKS Table of n, a(n) for n=1..100. FORMULA Limit_{n->oo} (a(1) + a(2) + ... + a(n))/n = 1.354.... MATHEMATICA Nest[Join[#, Take[#, Length@ # - 1]] &, {1, 2}, 7] (* Michael De Vlieger, Oct 18 2017 *) PROG (PARI) v=[1, 2]; for(n=1, 10, l=length(v); w=vector(l-1, i, v[i]); v=concat(v, if(v[l]-1, concat(w), w))); a(n)=v[n]; CROSSREFS Cf. A293630, A293811. Sequence in context: A358005 A078316 A207668 * A055443 A003842 A095771 Adjacent sequences: A293835 A293836 A293837 * A293839 A293840 A293841 KEYWORD nonn AUTHOR Benoit Cloitre, Oct 17 2017 STATUS approved

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Last modified September 9 23:53 EDT 2024. Contains 375765 sequences. (Running on oeis4.)