A175306 Irregular array: row n contains A175307(n) terms. The first term of each row, a(n,1) = n. a(n,m) = the smallest integer > a(n,m-1) such that a(n,m), a(n,m)-1, and a(n,m)+1 are each coprime to all earlier terms in their row. The row terminates when a multiple of 2 or 3 is obtained.

1, 2, 2, 3, 4, 5, 7, 12, 6, 7, 9, 8, 9, 10, 11, 13, 15, 12, 13, 15, 14, 15, 16, 17, 19, 21, 18, 19, 21, 20, 21, 22, 23, 25, 27, 24, 25, 27, 26, 27, 28, 29, 31, 33, 30, 31, 33, 32, 33, 34, 35, 37, 47, 52, 36, 37, 39, 38, 39, 40, 41, 43, 45, 42, 43, 45, 44, 45, 46, 47, 49, 51, 48, 49, 51, 50, 51, 52, 53

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10102

Maple

A175306:= proc(n)
local R, last, k, P;
R:= n;
last:= n;
P:= n;
while igcd(last, 6)=1 do
  for k from last+1 do
    if igcd(k-1, P) = 1 and igcd(k, P) = 1 and igcd(k+1, P) =1 then
      R:= R, k; last:= k; P:= P*k; break
    fi
  od
od;
R
end proc:
map(A175306, [$1..100]); # Robert Israel, Feb 10 2017

Mathematica

row[n_] := Module[{R = {n}, last = n, k, P = n}, While[GCD[last, 6] == 1, For[k = last + 1, True, k++, If[GCD[k - 1, P] == 1 && GCD[k, P] == 1 && GCD[k + 1, P] == 1, AppendTo[R, k]; last = k; P = P k; Break[]]]]; R];
Array[row, 100] // Flatten (* Jean-François Alcover, Jul 25 2020, after Robert Israel *)

Crossrefs

Cf. A175307

Sequence in context: A034395 A032232 A378286 * A359348 A021993 A324743

Adjacent sequences: A175303 A175304 A175305 * A175307 A175308 A175309

Keyword

nonn,tabf

Author

Leroy Quet, Mar 26 2010

Status

approved