A132850 a(0)=1; a(n) = the smallest prime dividing (n+a(n-1)), for n>=1.

1, 2, 2, 5, 3, 2, 2, 3, 11, 2, 2, 13, 5, 2, 2, 17, 3, 2, 2, 3, 23, 2, 2, 5, 29, 2, 2, 29, 3, 2, 2, 3, 5, 2, 2, 37, 73, 2, 2, 41, 3, 2, 2, 3, 47, 2, 2, 7, 5, 2, 2, 53, 3, 2, 2, 3, 59, 2, 2, 61, 11, 2, 2, 5, 3, 2, 2, 3, 71, 2, 2, 73, 5, 2, 2, 7, 83, 2, 2, 3, 83, 2, 2, 5, 89, 2, 2, 89, 3, 2, 2, 3, 5, 2, 2

Offset: 0

Author

Leroy Quet, Nov 21 2007

Keywords

• nonn

Comments

a(4n+1) = a(4n+2) = 2, for all n >= 0. a(4n) and a(4n+3) are odd primes, for all n >= 0.

Examples

			a(8) + 9 = 11 + 9 = 20. The smallest prime divisor of 20 is 2. So a(9) = 2.
		

Links

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

Crossrefs

Cf. A076561.

Programs

Mathematica

a = {1}; Do[AppendTo[a, FactorInteger[n + a[[ -1]]][[1, 1]]], {n, 1, 100}]; a (* Stefan Steinerberger, Nov 25 2007 *)
nxt[{n_,a_}]:={n+1,FactorInteger[n+1+a][[1,1]]}; Transpose[NestList[nxt,{0,1},100]][[2]] (* Harvey P. Dale, Jan 21 2015 *)

Extensions

More terms from Stefan Steinerberger, Nov 25 2007