A379529 a(0) = 0; for n>0, let MSD = Most Significant Digit and LSD = Least Significant Digit, set MSD(a(n)) = [10 - LSD(a(n-1))] mod 10 and let remaining digits of a(n) be such that a(n) is the least integer not yet present in the sequence. If LSD(a(n-1)) = 0 then the least integer not yet present in the sequence is chosen, whatever its MSD is.

0, 1, 9, 10, 2, 8, 20, 3, 7, 30, 4, 6, 40, 5, 50, 11, 90, 12, 80, 13, 70, 14, 60, 15, 51, 91, 92, 81, 93, 71, 94, 61, 95, 52, 82, 83, 72, 84, 62, 85, 53, 73, 74, 63, 75, 54, 64, 65, 55, 56, 41, 96, 42, 86, 43, 76, 44, 66, 45, 57, 31, 97, 32, 87, 33, 77, 34, 67, 35

Offset

0,3

Comments

Rearrangement of nonnegative integers.

a(n) = n for n = 0, 1, 67, 99, ...

Links

Paolo P. Lava, Table of n, a(n) for n = 0..10000

Example

a(0) = 0; a(1) = 1 because is the least number not yet present in the sequence; a(2) should start with [(10 - 1) mod 10] = [9 mod 10] = 9 and being 9 not yet present in the sequence then a(2) = 9; a(3) should start with [(10 - 9) mod 10] = [1 mod 10] = 1 but 1 is already present and the least integer we can choose is 10, so a(3) = 10; now LSD(a(3)) is 0 and we can simply choose the least number not yet present that is 2: therefore a(4) = 2; and so on.

Maple

P:=proc(q) local a, b, c, n, t, v; v:=[0]; t:=0; for n from 2 to q do a:=10-(v[n-1] mod 10) mod 10;
if a=0 then while numboccur(v, t)>0 do t:=t+1; od; v:=[op(v), t]; else
if numboccur(v, a)=0 then v:=[op(v), a]; else c:=-1; b:=a;
while numboccur(v, b)>0 do c:=c+1; if c=0 then b:=10*a; else b:=a*10^length(c)+c; fi; od;
v:=[op(v), b]; fi; fi; od; op(v); end: P(10^2);

Crossrefs

Cf. A010879.

Sequence in context: A158286 A126839 A341818 * A034058 A347181 A333774

Adjacent sequences: A379526 A379527 A379528 * A379530 A379531 A379532

Keyword

nonn,easy,base

Author

Paolo P. Lava, Dec 24 2024

Status

approved