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.

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

Author

Frank Buss (fb(AT)frank-buss.de), Feb 19 2002

Keywords

• nonn

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

• Mauro Fiorentini, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A068193 has the indices of the primes in this sequence. A066631 has the sequence of f's. Also see A067836.

Programs

Mathematica

<
				

MuPAD

f := 4:for n from 1 to 50 do a := f-numlib::prevprime(f-2):f := f*a:print(a) end_for

Extensions

Edited by Dean Hickerson, Jun 10 2002