A243063 - OEIS

%I #42 Sep 12 2022 13:07:28

%S 1,1,2,3,5,8,13,21,34,55,89,144,233,377,61,438,499,937,1436,2373,389,

%T 2762,3151,5913,964,6877,7841,14718,22559,37277,59836,97113,156949,

%U 25462,182411,27873,21284,49157,7441,56598,6439,6337,12776,19113,31889,512,3241

%N Numbers generated by a Fibonacci-like sequence in which zeros are suppressed.

%C Let x(1) = 1, x(2) = 1, then begin the sequence x(i) = no-zero(x(i-2) + x(i-1)), where the function no-zero(n) removes all zero digits from n.

%C The sequence behaves like a standard Fibonacci sequence until step 15, where x = no-zero(233 + 377) = no-zero(610) = 61. At step 16, x = 377 + 61 = 438. The sequence then proceeds until step 927, where x = no-zero(224 + 377) = no-zero(601) = 61. Therefore at step 928, x = 377 + 61 = 438 and the sequence repeats.

%H Anthony Sand, <a href="/A243063/b243063.txt">Table of n, a(n) for n = 1..927</a>

%H <a href="/index/Rec#order_912">Index entries for linear recurrences with constant coefficients</a>, order 912.

%F x(i) = no-zero(x(i-2) + x(i-1)). For example, no-zero(233 + 377) = no-zero(610) = 61.

%e x(3) = x(1) + x(2) = 1 + 1 = 2.

%e x(4) = x(2) + x(3) = 1 + 2 = 3.

%e x(15) = no-zero(x(13) + x(14)) = no-zero(233 + 377) = no-zero(610) = 61.

%e x(16) = 377 + 61 = 438.

%p noz:=proc(n) local a,t1,i,j; a:=0; t1:=convert(n,base,10); for i from 1 to nops(t1) do j:=t1[nops(t1)+1-i]; if j <> 0 then a := 10*a+j; fi; od: a; end; # A004719

%p t1:=[1,1]; for n from 3 to 100 do t1:=[op(t1),noz(t1[n-1]+t1[n-2])]; od: t1; # _N. J. A. Sloane_, Jun 11 2014

%t Nest[Append[#, FromDigits@ DeleteCases[IntegerDigits[Total@ #[[-2 ;; -1]] ], _?(# == 0 &)]] &, {1, 1}, 45] (* _Michael De Vlieger_, Jun 27 2020 *)

%t nxt[{a_,b_}]:={b,FromDigits[DeleteCases[IntegerDigits[a+b],0]]}; NestList[nxt,{1,1},50][[All,1]] (* _Harvey P. Dale_, Sep 12 2022 *)

%Y Cf. A000045, A004719, A242350, A243657, A243658, A306773.

%K nonn,base

%O 1,3

%A _Anthony Sand_, Jun 09 2014