A259828 a(1)=a(2)=2; thereafter, a(n)=gpf(1+a(n-1)a(n-2)), where gpf is greatest prime factor.

2, 2, 5, 11, 7, 13, 23, 5, 29, 73, 353, 859, 8423, 92761, 856717, 126948763, 122613509, 2102184467, 2530079, 2659346387041447, 334098941853251, 148080802321968921649521449033, 6863460080030077, 1678153631189331624730247, 7109839787546601453693131222417760271, 5808110138398623777046165714073

Offset

1,1

Links

Table of n, a(n) for n=1..26.

Mathematica

a = {2, 2}; Do[AppendTo[a, FactorInteger[1 + a[[n - 1]] a[[n - 2]]][[-1, 1]]], {n, 3, 26}]; a (* Michael De Vlieger, Aug 05 2015 *)
nxt[{a_, b_}] := {b, FactorInteger[a*b + 1][[-1, 1]]}; NestList[nxt, {2, 2}, 30][[All, 1]] (* Harvey P. Dale, Aug 03 2018 *)

Prog

(Sage)
def gpf(n):
    return (factor(n)[-1])[0]
def A259828vec(m): # m>2=f
    f=2
    v=[2, 2]
    for i in range(f, m):
        v.append(gpf(1+v[i-1]*v[i-2]))
    return v
(PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f];
first(m)=my(v=vector(m)); v[1]=2; v[2]=2; for(i=3, m, v[i]=gpf(1+v[i-1]*v[i-2])); v;

Crossrefs

Cf. A260725, A000945.

Sequence in context: A233018 A209100 A208864 * A366094 A104080 A336269

Adjacent sequences: A259825 A259826 A259827 * A259829 A259830 A259831

Keyword

nonn

Author

Anders Hellström, Aug 05 2015

Extensions

Terms a(20)-a(26) from Michael De Vlieger, Aug 05 2015

Status

approved