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a(n+1) = a(n)+greatest prime divisor of a(n-1).
4

%I #7 Jan 15 2016 18:33:20

%S 1,1,2,3,5,8,13,15,28,33,40,51,56,73,80,153,158,175,254,261,388,417,

%T 514,653,910,1563,1576,2097,2294,2527,2564,2583,3224,3265,3296,3949,

%U 4052,4411,5424,5825,5938,6171,9140,9157,9614,18771,18794,25051,34448,34495

%N a(n+1) = a(n)+greatest prime divisor of a(n-1).

%H Harvey P. Dale, <a href="/A078695/b078695.txt">Table of n, a(n) for n = 1..1000</a>

%e a(12) = 51 = 3*17, a(13) = 56, so a(14) = 56+17 = 73

%t nxt[{a_,b_}]:={b,b+FactorInteger[a][[-1,1]]}; Transpose[NestList[nxt,{1,1},50]][[1]] (* _Harvey P. Dale_, Jan 15 2016 *)

%Y Cf. A000045.

%K easy,nonn

%O 1,3

%A _Miklos Kristof_, Dec 18 2002

%E More terms from _Robert G. Wilson v_, Dec 19 2002