A249399 Start with a(1) = 1 then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(n-1),a(n)).
1, 2, 4, 5, 10, 20, 8, 16, 25, 50, 40, 32, 64, 80, 100, 125, 200, 160, 128, 250, 400, 320, 256, 500, 625, 1000, 800, 640, 512, 1024, 1250, 2000, 1280, 1600, 2500, 3125, 5000, 3200, 2048, 2560, 4000, 6250, 10000, 6400, 4096, 5120, 8000, 10240, 8192, 12500, 15625
Offset: 1
Examples
a(1) = 1; a(2) = 2 -> 12 /2 = 6; Now we cannot use 3 as the next term because it does not divide 23. a(3) = 4 -> 24 / 4 = 6; a(4) = 5 -> 45 / 5 = 9; Again, 3, 6, 7, 8 and 9 cannot be used as the next term. a(5) = 10 -> 510 / 10 = 51; a(6) = 20 -> 1020 / 20 = 51; a(7) = 8 -> 208 / 8 = 26; etc.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..100
Programs
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Maple
with(numtheory); P:=proc(q) local a,b,k,n; print(1); a:=1; b:={1}; for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1 then if type((a*10^(1+ilog10(n))+n)/n,integer) then a:=n; b:=b union {n}; print(n); break; fi; fi; od; od; end: P(10^12);
Comments