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A352340
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a(n) is the sum of digits of n in the maximal Pell representation of n (A352339).
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5
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0, 1, 1, 2, 2, 3, 4, 2, 3, 3, 4, 5, 3, 4, 4, 5, 3, 4, 5, 3, 4, 4, 5, 6, 4, 5, 5, 6, 4, 5, 6, 4, 5, 5, 6, 7, 5, 6, 6, 7, 8, 4, 5, 5, 6, 4, 5, 6, 4, 5, 5, 6, 7, 5, 6, 6, 7, 5, 6, 7, 5, 6, 6, 7, 8, 6, 7, 7, 8, 9, 5, 6, 6, 7, 5, 6, 7, 5, 6, 6, 7, 8, 6, 7, 7, 8, 6
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OFFSET
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0,4
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LINKS
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FORMULA
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MATHEMATICA
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pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; pellp[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; IntegerDigits[Total[3^(s - 1)], 3]]; a[n_] := Module[{v = pellp[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] > 0 && v[[i + 1]] == 0 && v[[i + 2]] < 2, v[[i ;; i + 2]] += {-1, 2, 1}; If[i > 2, i -= 3]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, 0, Total[v[[i[[1, 1]] ;; -1]]]]]; Array[a, 100, 0]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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