A328503 - OEIS

%I #36 Oct 15 2023 18:38:19

%S 1,3,6,2,7,13,20,2,11,21,3,15,3,17,32,2,19,37,56,2,23,45,3,27,3,29,56,

%T 2,31,61,92,2,35,5,40,2,39,3,42,2,43,85,5,49,7,53,100,2,51,3,54,2,55,

%U 5,60,2,59,117,3,63,3,65,5,69,3,69,3,71,140,2,73

%N a(1) = 1; a(n) = the least prime factor of a(n-1) if a(n-1) is a composite number, otherwise a(n) = a(n-1) + n.

%C  Will all prime numbers appear in this sequence?

%H Robert Israel, <a href="/A328503/b328503.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7)=20, a(8) = least prime factor of 20 = 2.

%e a(9)=11, a(10) = 11+10 = 21.

%p f:= proc(n) local q; option remember;

%p   q:= procname(n-1);

%p   if isprime(q) then q+n

%p   else min(numtheory:-factorset(q))

%p   fi

%p end proc:

%p f(1):= 1: f(2):=3:

%p map(f, [$1..100]); # _Robert Israel_, Oct 25 2019

%t a[1] = 1; a[n_] := a[n] = If[CompositeQ[a[n - 1]], FactorInteger[a[n - 1]][[1, 1]], a[n - 1] + n]; Array[a, 100] (* _Amiram Eldar_, Oct 23 2019 *)

%t nxt[{n_,a_}]:={n+1,If[CompositeQ[a],FactorInteger[a][[1,1]],a+n+1]}; NestList[nxt,{1,1},70] [[;;,2]] (* _Harvey P. Dale_, Oct 15 2023 *)

%o (PARI) for (n=1, 71, print1 (v=if (n==1, 1, bigomega(f=factor(v))>1, f[1,1], v+n) ", ")) \\ _Rémy Sigrist_, Oct 23 2019

%Y Cf. A020639, A326935.

%K nonn,look

%O 1,2

%A _Ali Sada_, Oct 22 2019