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Numbers k such that m*2^k+1 is not prime for all coefficients m in the range 0<=m<=k.
6

%I #15 Mar 25 2019 07:12:31

%S 9,10,22,31,86,99,100,101,113,114,115,130,135,136,149,154,169,217,218,

%T 223,224,283,301,309,358,383,384,422,423,424,425,426,449,457,473,495,

%U 505,506,541,542,548,549,564,571,572,573,628,668,670,681,682,683,713

%N Numbers k such that m*2^k+1 is not prime for all coefficients m in the range 0<=m<=k.

%H Robert Israel, <a href="/A061410/b061410.txt">Table of n, a(n) for n = 1..285</a>

%p filter:= n -> andmap(not isprime, [seq(m*2^n+1,m=1..n)]):

%p select(filter, [$1..1000]); # _Robert Israel_, Dec 10 2017

%t okQ[n_] := AllTrue[2^n Range[n] + 1, CompositeQ];

%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Mar 25 2019 *)

%o (PARI) isok(n) = {for (m=0, n, if (isprime(m*2^n+1), return (0));); return (1);} \\ _Michel Marcus_, Dec 11 2017

%Y Cf. A061411, A061412, A061413, A061414, A061415.

%K nonn

%O 1,1

%A _Patrick De Geest_, May 15 2001