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A372467
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a(n) = log_2(A372466(n) + 1).
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3
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0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2
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OFFSET
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1,7
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (d(1) + Sum_{k>=2} (k * (d(k) - d(k-1))) / A327839 = 1.12132865776925625956..., where d(k) = Product_{p prime} (1 - 1/p + Sum_{i=1..k} (1/p^(2^i-1)-1/p^(2^i))).
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MATHEMATICA
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pow2Q[n_] := n == 2^IntegerExponent[n, 2]; f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, pow2Q[# + 1] &], IntegerExponent[Max @@ e + 1, 2], Nothing]]; f[1] = 0; Array[f, 150]
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PROG
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(PARI) ispow2(n) = n >> valuation(n, 2) == 1;
lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = factor(k)[, 2]; if(ispow2(vecprod(apply(x -> x + 1, e))), print1(valuation(vecmax(e) + 1, 2), ", "))); }
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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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