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, 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
Offset: 1
Keywords
Examples
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.
Links
- Samuel Harkness, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A358921.
Programs
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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 *) -
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
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