[seqfan] Re: 1,2,3,5,8,13,21,4,25,29,6,...

Hans Havermann gladhobo at bell.net
Fri Sep 13 16:40:28 CEST 2019


EA: "Start S with a(1) = 1 and a(2) = 2. Now if a(n) and a(n+1) don't share any digit, then a(n+2) = a(n) + a(n+1). Else a(n+2) = the smallest integer not yet in S."

Almost all adjacent terms share a digit so let's focus on those terms that are sums (term#,sum). From (3,3) to (107,239) there are 43 such. From here on to term 10^3 are 16 more; from 10^3 to 10^4, 16 more; from 10^4 to 10^5, 16 more:

(125,198)    (1013,1998)    (10015,19998)
(212,399)    (2007,3999)    (20009,39999)
(213,599)    (2008,5999)    (20010,59999)
(215,800)    (2010,8000)    (20012,80000)
(310,599)    (3009,5999)    (30011,59999)
(311,899)    (3010,8999)    (30012,89999)
(313,1200)   (3012,12000)   (30014,120000)
(411,798)    (4011,7998)    (40013,79998)
(412,1198)   (4012,11998)   (40014,119998)
(513,999)    (5013,9999)    (50015,99999)
(514,1499)   (5014,14999)   (50016,149999)
(614,1198)   (6014,11998)   (60016,119998)
(615,1798)   (6015,17998)   (60017,179998)
(715,1399)   (7016,13999)   (70018,139999)
(716,2099)   (7017,20999)   (70019,209999)
(815,1600)   (8017,16000)   (80019,160000)

Perhaps this continues forever.


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