A317547 Decimal expansion of f(0) such that f(n) = log(abs(f(n-1))) > 0 iff n is a prime number (negated).

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)

Links

Table of n, a(n) for n=-1..98.

J. Maiga, Fun with signed nested exponentials and the prime numbers

Jon Maiga, Plot of f(n) with n up to 4000.

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

Cf. A010051, A201942.

Sequence in context: A124392 A144446 A121416 * A089329 A213053 A200236

Adjacent sequences: A317544 A317545 A317546 * A317548 A317549 A317550

Keyword

nonn,cons

Author

Jon Maiga, Jul 30 2018

Status

approved