A244890 "Stringed numbers": see Comments for definition.

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

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: A338829 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