A031441 a(0) = 3; for n > 0, a(n) is the greatest prime factor of PreviousPrime(a(n-1))*a(n-1)-1 where PreviousPrime(prime(k))=prime(k-1).

3, 5, 7, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23, 109, 17, 11, 19, 23

Offset: 0

Author

Yasutoshi Kohmoto

Keywords

• nonn
• easy
• nice

Examples

			To get a(3) we compute PreviousPrime(7)=5, 5*7-1=34, greatest prime factor of 34 is 17, so a(3)=17.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A034970, A031442.

Programs

Mathematica

a[0] = 3; a[n_] := a[n] = FactorInteger[ NextPrime[ a[n-1], -1]*a[n-1] - 1][[-1, 1]]; Table[a[n], {n, 0, 66}] (* Jean-François Alcover, Mar 09 2012 *)
NestList[FactorInteger[NextPrime[#,-1]*#-1][[-1,1]]&,3,70] (* Harvey P. Dale, Dec 13 2012 *)

Extensions

More terms from James Sellers