A280894 a(n) is the largest prime factor of the concatenation of a(n-2) and a(n-1), with a(1)=1 and a(2)=2.
1, 2, 3, 23, 19, 773, 13, 25771, 1325771, 85903775257, 2599552664779907, 4078014120856770452857, 770310365288124131869, 47072294862890243358278834974724275093, 8735279620054327668810964663269852011597, 1500540910023123440069025527770773118908806062201
Offset: 1
Examples
The largest prime factor of concat(1,2) = 12 is 3: then a(3) = 3; The largest prime factor of concat(2,3) = 23 is 23: then a(4) = 23; etc.
Links
- Daniel Suteu, Table of n, a(n) for n = 1..21 (terms 1..17 from Michael De Vlieger)
Programs
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Maple
with(numtheory): P:= proc(q) local a,b,c,d,k,n; print(1); print(2); d:=2; a:=12; for n from 3 to q do b:=ifactors(a)[2]; c:=0; for k from 1 to nops(b) do if b[k][1]>c then c:=b[k][1]; fi; od; a:=d*10^(ilog10(c)+1)+c; d:=c; print(c); od; end: P(10^2);
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Mathematica
a = {1, 2}; Do[AppendTo[a, FactorInteger[FromDigits@ Flatten@ Map[IntegerDigits, Take[a, -2]]][[-1, 1]]], {13}]; a (* Michael De Vlieger, Jan 10 2017 *) nxt[{a_,b_}]:={b,FactorInteger[a*10^IntegerLength[b]+b][[-1,1]]}; NestList[nxt,{1,2},15][[;;,1]] (* Harvey P. Dale, Mar 09 2025 *)
Extensions
a(16) from Michael De Vlieger, Jan 10 2017