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A293273 a(n) is the smallest positive k <> n such that f(k) is divisible by f(n) where f = A005132, or 0 if no such k exists. 1
2, 3, 8, 3, 9, 35, 43, 15, 20, 11, 28, 7, 32, 21, 83, 15, 69, 26, 152, 24, 116, 47, 44, 20, 48, 18, 43, 59, 30, 63, 20, 104, 41, 71, 39, 75, 72, 35, 35, 36, 33, 79, 92, 83, 96, 87, 100, 91, 245, 95, 239, 67, 276, 19, 119, 63, 109, 57, 103, 51, 185, 45, 139, 35, 145, 86, 415, 84, 192, 82, 184, 80, 180, 78, 176 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: a(n) > 0 for all n.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Logarithmic scatterplot of the first 100000 terms

Rémy Sigrist, Scatterplot of the first 100000 terms of the first difference

EXAMPLE

a(6) = 35 because A005132(35) = 78 is divisible by A005132(6) = 13 and 78 is the smallest positive number which is not equal to 6 with this property.

MAPLE

N:= 10^4: # to use A005132(n) for n = 1..N

S:= {0}:

A5132:= Array(0..N):

A5132[0]:= 0:

for n from 1 to N do

  v:= A5132[n-1]-n;

  if v < 0 or member(v, S) then v:= A5132[n-1]+n fi;

  A5132[n]:= v;

  S:= S union {v};

od:

f:= proc(n) local k;

  for k from 1 to N do

    if k <> n and A5132[k] mod A5132[n] = 0 then return k fi

  od:

0

end proc:

Res:= NULL:

for n from 1 do

  v:= f(n);

  if v = 0 then break fi;

  Res:= Res, v;

od:

Res; # Robert Israel, Oct 10 2017

CROSSREFS

Cf. A005132, A057167.

Sequence in context: A154826 A155994 A011162 * A079555 A100870 A210688

Adjacent sequences:  A293270 A293271 A293272 * A293274 A293275 A293276

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Oct 10 2017

STATUS

approved

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Last modified October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)