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A317547
Decimal expansion of f(0) such that f(n) = log(abs(f(n-1))) > 0 iff n is a prime number (negated).
1
2, 1, 7, 2, 2, 6, 8, 9, 8, 3, 5, 6, 1, 2, 0, 8, 4, 2, 7, 4, 3, 0, 1, 9, 2, 8, 8, 2, 3, 3, 3, 5, 3, 8, 8, 8, 5, 4, 1, 4, 4, 1, 0, 2, 2, 3, 3, 0, 0, 6, 1, 7, 3, 6, 2, 2, 9, 6, 9, 4, 2, 0, 1, 4, 9, 3, 8, 4, 4, 9, 9, 7, 7, 8, 5, 1, 9, 2, 9, 7, 1, 1, 9, 3, 5, 5, 0, 3, 2, 2, 2, 0, 5, 9, 0, 8, 5, 8, 8, 8
OFFSET
-1,1
COMMENTS
If f(0)=A201942, f(n) will generate the odd numbers.
From Jon Maiga, May 02 2019: (Start)
The image shows f(n), note the symmetry around -LambertW(1) (~ -0.57). For example, all values in the lowest positive horizontal 'segment' (f(n) ~ 0.2) consists of the lesser twin primes (A001359). The corresponding segment at f(n)~-1.2 are n such that n+1 and n+3 are primes (A144834).
With 256-digit precision for f(0), f(n) will correctly decode all n up to 1069, which is the 180th prime number.
(End)
FORMULA
Equals lim_{n->oo} sf(0)*exp(sf(1)*exp(...sf(n-1)*exp(sf(n)))) where sf(n)=2*(A010051(n)-1).
EXAMPLE
-0.02172268983561208427430192882333538885414410223300617362296942014938449977851...
MATHEMATICA
f0[n_] := (v = 0; For[i = n, i >= 0, i--, v = If[PrimeQ[i], 1, -1]*Exp[v]]; v);
RealDigits[f0[1000], 10, 100][[1]]
CROSSREFS
Sequence in context: A124392 A144446 A121416 * A089329 A213053 A200236
KEYWORD
nonn,cons
AUTHOR
Jon Maiga, Jul 30 2018
STATUS
approved