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 A359728 a(1) = 1; a(n) is the smallest positive number not among the first k terms where k is the number of times a(n-1) has occurred. 1
 1, 2, 2, 3, 2, 3, 3, 3, 4, 2, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 5, 2, 4, 5, 3, 4, 5, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 2, 4, 5, 6, 3, 5, 6, 3, 5, 6, 4, 5, 6, 4, 5, 6, 4, 6, 4, 6, 4, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A new number is always followed by a 2. LINKS Samuel Harkness, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) is 3 because the previous term (2) appears two times; we therefore look at the first 2 terms (1,2). 3 is the smallest number not among them, so a(4) is 3. a(21) is 5: We see that a(20)=4 appears 9 times; the smallest number not among the first 9 terms (1,2,2,3,2,3,3,3,4) is 5. MATHEMATICA K = {1}; While[Length@K < 87, T = Take[K, Count[K, Last@K]]; i = 1; While[MemberQ[T, i], i++]; AppendTo[K, i]]; Print[K] (* Samuel Harkness, Mar 12 2023 *) PROG (PARI) lista(nn) = my(va=vector(nn)); va[1] = 1; for (n=2, nn, my(k=#select(x->(x==va[n-1]), va)); my(vb=Vec(va, k), m); for(j=1, vecmax(vb)+1, if (! #select(x->(x==j), vb), m=j; break)); va[n] = m; ); va; \\ Michel Marcus, Jan 13 2023 CROSSREFS Cf. A358921. Sequence in context: A358550 A126071 A338292 * A217865 A185166 A276555 Adjacent sequences: A359725 A359726 A359727 * A359729 A359730 A359731 KEYWORD nonn AUTHOR Neal Gersh Tolunsky, Jan 11 2023 STATUS approved

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Last modified May 27 21:52 EDT 2024. Contains 372882 sequences. (Running on oeis4.)