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a(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1).
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%I #14 Sep 23 2020 02:43:10

%S 1,1,11,37,379,37379,130369,463,12277,4210207,1015309,42102071015309,

%T 7522851571,39903394005601130021,747580650949733,

%U 2601211879473948668292638737,16287160151410310678021523908384898241043,37391601140774556436246253

%N a(1) = a(2) = 1, a(n) is largest prime factor of concatenation of a(n - 2) and a(n - 1).

%H Sean A. Irvine, <a href="/A034969/b034969.txt">Table of n, a(n) for n = 1..26</a>

%e a(6) = 37379 because the concatenation of a(4) and a(5) is 37379, a prime number.

%e a(7) = 130369 because the concatenation of a(5) and a(6) is 37937379 = 3 * 97 * 130369.

%t nxt[{a_,b_}]:={b,FactorInteger[FromDigits[Flatten[IntegerDigits[ {a,b}]]]][[-1,1]]}; Transpose[NestList[nxt,{1,1},18]][[1]] (* _Harvey P. Dale_, Nov 24 2012 *)

%K nonn,base,nice

%O 1,3

%A _Erich Friedman_

%E Corrected and extended by _Harvey P. Dale_, Nov 24 2012