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A346778
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Least k >= 1 such that {b(1), b(2), ..., b(k)} = {n, n-1, ..., n-k+1} and b(k+1) = n-k where b(1..n) is row n of A088643, or k = 0 if no such k >= 1 exists.
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5
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0, 1, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 6, 12, 1, 1, 4, 6, 1, 8, 1, 1, 4, 1, 6, 22, 1, 9, 10, 1, 1, 4, 6, 1, 8, 1, 1, 4, 6, 1, 8, 1, 18, 9, 1, 9, 10, 16, 1, 18, 1, 1, 4, 1, 1, 4, 1, 6, 12, 11, 27, 14, 62, 1, 17, 1, 18, 18, 1, 1, 4, 6, 8, 10, 1, 1, 4, 6, 1, 8, 19
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OFFSET
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1,5
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COMMENTS
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Equivalently, least k such that {b(1), b(2), ..., b(k)} = {n, n-1, ..., n-k+1} and {b(1), b(2), ..., b(k), b(k+1)} = {n, n-1, ..., n-k+1, n-k}.
Since any row n of A088643 is a permutation of [1..n] having 1 as last term (conjectured), one always has a(n) <= n - 1. - M. F. Hasler, Aug 04 2021
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LINKS
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MATHEMATICA
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t[n_, 1] := n;
t[n_, k_] := t[n, k] = For[m = n-1, m >= 1, m--, If[PrimeQ[m + t[n, k-1]] && FreeQ[Table[t[n, j], {j, 1, k-1}], m], Return[m]]];
a[n_] := If[n == 1, 0, Module[{r, g}, r = Table[t[n, k], {k, 1, n}]; For[g = 1, g <= n-1, g++, If[Union@r[[1 ;; g]] == Range[n-g+1, n] && r[[g+1]] == n-g, Return[g]]]]];
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PROG
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(PARI) apply( {A346778(n, r=A088643_row(n))=for(g=1, n-1, Set(r[1..g])==[n-g+1..n] && r[g+1]==n-g && return(g))}, [1..99]) \\ M. F. Hasler, Aug 04 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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