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A244890 "Stringed numbers": see Comments for definition. 1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 201, 300, 301, 400, 401, 500, 501, 600, 601, 700, 701, 800, 801, 900, 901, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Supoose n is the k-digit number d_1 d_2 ... d_k. Form a graph with k nodes labeled 1, 2, ..., k. Join node i to node j by a directed edge whenever |j-i| = 1 + d_i. Then n is a stringed number iff the graph has a Hamiltonian path.

Single-digit numbers are trivially stringed.

REFERENCES

Eric Angelini, Posting to Sequence Fans Mailing List, Jul 10 2014; with additional comments from Robert Israel.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10001

EXAMPLE

If n = 2014 the graph has nodes 1,2,3,4 with edges 1->4 (since 4-1=d_1+1=3), 2->1 (since 2-1=d_2+1=1), 2->3 (since 3-2=d_2+1=1), 3->1 (since 3-1=d_3+1=2) , and there is a Hamiltonian path 2->3->1->4, so 2014 is stringed.

MAPLE

Stringed:= proc(n)

uses GraphTheory;

local L, G, E, d;

L:= convert(n, base, 10);

d:= nops(L);

E:= select(e -> e[2] <= d and e[2] >= 1,   {seq(seq([i, i+s*(1+L[i])], s=[1, -1]), i=1..d)})

  union {seq([0, i], i=1..d)} union {seq([i, 0], i=1..d)};;

G:= Digraph([$0..d], E);

IsHamiltonian(G);

end proc;

select(Stringed, {$0..2020});

# Robert Israel, Jul 10 2014

CROSSREFS

Sequence in context: A175396 A107085 A212499 * A032945 A236402 A052018

Adjacent sequences:  A244887 A244888 A244889 * A244891 A244892 A244893

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jul 13 2014

EXTENSIONS

Corrected and extended by Robert Israel, Jul 10 2014

STATUS

approved

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Last modified August 10 12:19 EDT 2020. Contains 336379 sequences. (Running on oeis4.)