A126638 - OEIS

%I #19 Jun 01 2022 01:53:21

%S 4,9,25,26,27,35,38,39,49,50,51,77,80,81,91,92,93,95,98,99,115,116,

%T 117,119,121,122,123,125,128,129,133,134,135,143,146,147,155,158,159,

%U 161,164,165,169,172,175,177,178,185,187,188,189,205,206,207,209,212,213

%N a(n) is larger than a(n-1), not prime and coprime to a(n-1) and a(n-2).

%H Harvey P. Dale, <a href="/A126638/b126638.txt">Table of n, a(n) for n = 1..1000</a>

%e a(7) = 38 because it is the next composite number larger than 35 (a(6)) that shares no factors in common with 35 and 27 (a(5)).

%p with(numtheory); i:=4; j:=9; k:=10; while(k < 100) do while(order(k, i) = FAIL or order(k,j) = FAIL or isprime(k)) do k:=k+1; end do; print(k); i:= j; j:=k; k:=k+1; end do;

%t f[l_List] := Block[{k = l[[ -1]] + 1},While[PrimeQ[k] || GCD[k, l[[ -1]]*l[[ -2]]] > 1, k++ ];Append[l, k]];Nest[f, {4, 9}, 56] (* _Ray Chandler_, Feb 14 2007 *)

%t nxt[{a_,b_}]:=Module[{k=b+1},While[PrimeQ[k]||!CoprimeQ[a,k] || !CoprimeQ[ b,k],k++];{b,k}]; NestList[nxt,{4,9},60][[All,1]] (* _Harvey P. Dale_, Aug 31 2021 *)

%Y Cf. A051884.

%K nonn

%O 1,1

%A _Ben Paul Thurston_, Feb 08 2007

%E Extended by _Ray Chandler_, Feb 14 2007