



3, 5, 9, 11, 23, 29, 33, 35, 39, 41, 51, 53, 65, 69, 81, 83, 89, 95, 99, 105, 113, 119, 131, 135, 155, 173, 179, 183, 189, 191, 209, 221, 231, 233, 239, 243, 245, 251, 261, 273, 281, 293, 299, 303, 309, 323, 329, 359, 371, 375, 393, 411, 413, 419, 429
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OFFSET

1,1


COMMENTS

Previous name was: The A_1primes (Archimedes_1 primes).
We have: (1) N is an A_1prime iff N is odd, p=2N+1 is a prime number and only one of +2 and 2 generates Z_p^* (the multiplicative group of Z_p); (2) N is an A_1prime iff p=2N+1 is a prime number and exactly one of the following holds: (a) N == 1 (mod 4) and +2 generates Z_p^* but 2 does not, (b) N == 3 (mod 4) and 2 generates Z_p^* but +2 does not.
The A_1primes are the odd T or Twistprimes (the Tprimes are the same as the Queneaunumbers, A054639). For the related A_0, A^+_1 and A^_1primes, see A163777, A163779 and A163780. Considered as a set, the present sequence is the union of the A^+_1primes (A163779) and the A^_1primes (A163780). It is also equal to the difference of A054639 and the A_0primes (A163777).


LINKS



MATHEMATICA

follow[s_, f_] := Module[{t, k}, t = f[s]; k = 1; While[t>s, k++; t = f[t]]; If[s == t, k, 0]];
okQ[n_] := n>1 && n == follow[1, Function[j, Ceiling[n/2] + (1)^j*Ceiling[ (j1)/2]]];


PROG

(PARI)
Follow(s, f)={my(t=f(s), k=1); while(t>s, k++; t=f(t)); if(s==t, k, 0)}
ok(n)={n>1 && n==Follow(1, j>ceil(n/2) + (1)^j*ceil((j1)/2))}
(PARI)
ok(n)={n>1 && n%2==1 && isprime(2*n+1) && znorder(Mod(2, 2*n+1)) == if(n%4==3, n, 2*n)}


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



