A130570 Primes of the form k*2^m + 1 for k odd, m >=1, that are not Proth primes (A080076) (2^m <= k).

7, 11, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331

Offset: 1

Author

Jani Melik, Aug 10 2007

Keywords

• nonn

Examples

			a(1)=7 because 7 is prime, 7 = 3*2^1 + 1 and 2^1 <= 3,
a(2)=11 because 11 is prime, 11 = 5*2^1 + 1 and 2^1 <= 5,
a(3)=19 because 19 is prime, 19 = 9*2^1 + 1 and 2^1 <= 9, ...
		

Crossrefs

Cf. A080075.

Programs

Maple

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);
# Second Maple program
q := n -> (isprime(n) and n >= 2^(2*padic:-ordp(n-1,2))):
select(q, [$3..331])[]; # Lorenzo Sauras Altuzarra, Mar 03 2023

PARI

isok(p) = if (isprime(p), my(m=valuation(p-1,2)); (m>=1) && ((p-1) >= 4^m)); \\ Michel Marcus, Mar 03 2023