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A248025
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Lexicographically earliest permutation of the positive integers such that the first digit of a(n+1) is the digital root of a(n).
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6
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1, 10, 11, 2, 20, 21, 3, 30, 31, 4, 40, 41, 5, 50, 51, 6, 60, 61, 7, 70, 71, 8, 80, 81, 9, 90, 91, 12, 32, 52, 72, 92, 22, 42, 62, 82, 13, 43, 73, 14, 53, 83, 23, 54, 93, 33, 63, 94, 44, 84, 34, 74, 24, 64, 15, 65, 25, 75, 35, 85, 45, 95, 55, 16, 76, 46, 17, 86, 56, 26, 87, 66, 36, 96
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
E. Angelini, Fun and quick permutation (with a digital root), SeqFan list, Sep 29 2014.
Index entries for sequences that are permutations of the natural numbers
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MATHEMATICA
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Nest[Append[#, Block[{k = 1, r = Mod[#[[-1]], 9] + 9 Boole[Mod[#[[-1]], 9] == 0]}, While[Nand[FreeQ[#, k], IntegerDigits[k][[1]] == r], k++]; k]] &, {1}, 73] (* Michael De Vlieger, Oct 15 2020 *)
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PROG
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(PARI) a(n, S=1, u=2)={for(i=1, n, print1(S", "); S=(S-1)%9+1; for(k=1, 9e9, bittest(u, k)&&next; S==digits(k)[1]||next; u+=1<<S=k; break)); S}
(Haskell)
import Data.List (delete)
a248025 n = a248025_list !! (n-1)
a248025_list = 1 : f 1 [2..] where
f x zs = g zs where
g (y:ys) = if a000030 y == a010888 x
then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Sep 30 2014
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CROSSREFS
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Cf. A010888 (digital root); similar sequences: A248024,...
Cf. A247879 (inverse), A000030.
Sequence in context: A328752 A173821 A101807 * A303501 A289985 A065517
Adjacent sequences: A248022 A248023 A248024 * A248026 A248027 A248028
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KEYWORD
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nonn,base
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AUTHOR
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Eric Angelini and M. F. Hasler, Sep 29 2014
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STATUS
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approved
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