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A368131
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a(n) = floor(n * log(4/3) / log(3/2))
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1
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0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48
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OFFSET
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0,4
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COMMENTS
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Highest k with 3^(n+k) <= 4^n * 2^k.
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LINKS
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FORMULA
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a(n) = floor(n * log(3) / log(3/2)) - 2*n.
a(n) = floor(n * arctanh(1/7) / arctanh(1/5)).
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MATHEMATICA
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Table[Floor[n*Log[4/3]/Log[3/2]], {n, 0, 68}] (* James C. McMahon, Jan 27 2024 *)
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PROG
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(PARI) alist(N) = my(a=-1, b=1, k=0); vector(N, i, a+=2; b*=3; if(logint(b, 2) < a, a++; b*=3; k++); k); \\ note that i is n+1
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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