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A068192
Let a(1)=2, f(n) = 4*a(1)*a(2)*...*a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.
4
2, 3, 5, 7, 11, 13, 17, 19, 31, 29, 23, 41, 43, 37, 89, 59, 53, 67, 79, 71, 137, 109, 239, 167, 199, 47, 83, 97, 61, 373, 101, 179, 193, 131, 151, 73, 263, 593, 139, 113, 157, 103, 241, 181, 397, 233, 617, 311, 191, 229, 271, 269, 127, 223, 331, 337, 211, 163
OFFSET
1,1
COMMENTS
The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?
First 1000 terms are primes. - Mauro Fiorentini, Aug 01 2020
LINKS
MATHEMATICA
<<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)
f[1]=4; f[n_] := f[n]=f[n-1]a[n-1]; a[n_] := a[n]=Module[{i}, For[i=2, True, i++, If[ProvablePrimeQ[f[n]-i], Return[i]]]]
PROG
(MuPAD) f := 4:for n from 1 to 50 do a := f-numlib::prevprime(f-2):f := f*a:print(a) end_for
CROSSREFS
Cf. A068193 has the indices of the primes in this sequence. A066631 has the sequence of f's. Also see A067836.
Sequence in context: A177000 A117843 A293667 * A225083 A002200 A181561
KEYWORD
nonn
AUTHOR
Frank Buss (fb(AT)frank-buss.de), Feb 19 2002
EXTENSIONS
Edited by Dean Hickerson, Jun 10 2002
STATUS
approved