A260218 - OEIS

%I #32 Sep 30 2018 20:24:54

%S 2,3,2,5,2,3,2,17,2,3,2,5,2,3,2,257,2,3,2,5,2,3,2,17,2,3,2,5,2,3,2,

%T 65537,2,3,2,5,2,3,2,17,2,3,2,5,2,3,2,97,2,3,2,5,2,3,2,17,2,3,2,5,2,3,

%U 2,641,2,3,2,5,2,3,2,17,2,3,2,5,2,3

%N a(1) = 2; for n > 1 if n is even a(n) = spf(1 + Product_{odd m,m<n}a(m)), while if n is odd a(n) = spf(1 + Product_{even m,m<n}a(m)).

%H Antti Karttunen, <a href="/A260218/b260218.txt">Table of n, a(n) for n = 1..255</a>

%F It appears that for odd k, a(k) = 2 and for even k, a(k) = A002586(k/2). - _Michel Marcus_, Jul 20 2015

%t f[n_] := Block[{a = {2}, k, m}, Do[If[EvenQ@ k, AppendTo[a, FactorInteger[Product[a[[m]], {m, 1, k - 1, 2}] + 1][[1, 1]]], AppendTo[a, FactorInteger[Product[a[[m]], {m, 2, k - 1, 2}] + 1][[1, 1]]]], {k, 2, n}]; a]; f@ 80 (* _Michael De Vlieger_, Jul 20 2015 *)

%o (PARI) spf(n)=factor(n)[1, 1]

%o first(m)=my(v=vector(m), i, odd=2, even=1); v[1]=2; for(i=2, m, if(i%2==0, v[i]=spf(odd+1); even*=v[i], v[i]=spf(even+1); odd*=v[i])); v; /* _Anders Hellström_, Jul 19 2015 */

%o (PARI)

%o A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));

%o memoA260218 = Map();

%o A260218(n) = if(1==n,2,if(mapisdefined(memoA260218,n),mapget(memoA260218,n), my(k, m, v = if(!(n%2), k=1; m=1; while(k<n, m *= A260218(k); k += 2); A020639(m+1), k=2; m=1; while(k<n, m * A260218(k); k += 2); A020639(m+1))); mapput(memoA260218,n,v); (v))); \\ (An incrementally memoized version). _Antti Karttunen_, Sep 30 2018

%Y Cf. A000945, A005265, A007978, A053669, A075019, A258581.

%K nonn,less

%O 1,1

%A _Anders Hellström_, Jul 19 2015