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%I #10 Mar 03 2023 07:47:39
%S 7,11,19,23,29,31,37,43,47,53,59,61,67,71,73,79,83,89,101,103,107,109,
%T 127,131,137,139,149,151,157,163,167,173,179,181,191,197,199,211,223,
%U 227,229,233,239,251,263,269,271,277,281,283,293,307,311,313,317,331
%N Primes of the form k*2^m + 1 for k odd, m >=1, that are not Proth primes (A080076) (2^m <= k).
%e a(1)=7 because 7 is prime, 7 = 3*2^1 + 1 and 2^1 <= 3,
%e a(2)=11 because 11 is prime, 11 = 5*2^1 + 1 and 2^1 <= 5,
%e a(3)=19 because 19 is prime, 19 = 9*2^1 + 1 and 2^1 <= 9, ...
%p ts_neProth_prime:=proc(n) local i,j,k,a,am; k := 2: am:= [ ]: for i from 1 to n do for j from 1 by 2 to n do a := j*k^(i)+1: if (k^(i) <= j and isprime(a)=true) then am := [op(am), a ]: fi: od: od: RETURN( sort(am) ) end: ts_neProth_prime(400);
%p # Second Maple program
%p q := n -> (isprime(n) and n >= 2^(2*padic:-ordp(n-1,2))):
%p select(q, [$3..331])[]; # _Lorenzo Sauras Altuzarra_, Mar 03 2023
%o (PARI) isok(p) = if (isprime(p), my(m=valuation(p-1,2)); (m>=1) && ((p-1) >= 4^m)); \\ _Michel Marcus_, Mar 03 2023
%Y Cf. A080075.
%K nonn
%O 1,1
%A _Jani Melik_, Aug 10 2007
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