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A300999 Add to a(n) the first digit of a(n+1) to get a(n+2), with a(1) = 1 and a(2) = 2.

%I A300999 #20 Nov 19 2023 15:22:09
%S A300999 1,2,3,5,8,13,9,22,11,23,13,24,15,25,17,26,19,27,21,29,23,31,26,33,29,
%T A300999 35,32,38,35,41,39,44,43,48,47,52,52,57,57,62,63,68,69,74,76,81,84,89,
%U A300999 92,98,101,99,110,100,111,101,112,102,113,103,114,104,115,105,116,106,117,107,118,108,119
%N A300999 Add to a(n) the first digit of a(n+1) to get a(n+2), with a(1) = 1 and a(2) = 2.
%C A300999 The sequence, starting with a(1) = 1 and a(2) = 2, never enters into a loop.
%H A300999 Jean-Marc Falcoz, <a href="/A300999/b300999.txt">Table of n, a(n) for n = 1..10002</a>
%e A300999 a(1) + first digit of a(2) =  1 + 2 = a(3) =  3,
%e A300999 a(2) + first digit of a(3) =  2 + 3 = a(4) =  5,
%e A300999 a(3) + first digit of a(4) =  3 + 5 = a(5) =  8,
%e A300999 a(4) + first digit of a(5) =  5 + 8 = a(6) = 13,
%e A300999 a(5) + first digit of a(6) =  8 + 1 = a(7) =  9,
%e A300999 a(6) + first digit of a(7) = 13 + 9 = a(8) = 22,
%e A300999 a(7) + first digit of a(8) =  9 + 2 = a(9) = 11,
%e A300999 etc.
%t A300999 nxt[{a_,b_}]:={b,a+IntegerDigits[b][[1]]}; NestList[nxt,{1,2},80][[;;,1]] (* _Harvey P. Dale_, Nov 19 2023 *)
%o A300999 (PARI) a=vector(10^4); a[1]=1; a[2]=2; for(n=3, #a, a[n]=digits(a[n-1])[1]+a[n-2]); a \\ _Altug Alkan_, Mar 20 2018
%Y A300999 Cf. A267809.
%K A300999 nonn,base,easy
%O A300999 1,2
%A A300999 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 20 2018