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

0,2

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A076561.

Sequence in context: A097891 A097611 A135376 * A076561 A132851 A361119

Adjacent sequences: A132847 A132848 A132849 * A132851 A132852 A132853

Keyword

nonn

Author

Leroy Quet, Nov 21 2007

Extensions

More terms from Stefan Steinerberger, Nov 25 2007

Status

approved