2^k - 2m+1 = prime: (Was: Sum Of Primes Is Power Of Primes: Question)

[Maximilian Hasler]

On Sun, Apr 6, 2008 at 5:46 PM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

>  Could someone please calculate the sequence:
>
>  a(n) = the smallest positive integer k such that
>  2^k - 2n+1 is prime

Below a small script and what it prints, but I did not seriously check
its correctness.
However it seems to agree with A096502 (and up to a(6) also with A101462).
Maximilian

(17:45) gp > for(n=1,99,k=log(2*n)\log(2);while(!ispseudoprime(2^k++-2*n+1),);print(n"
"k))
1 2
2 3
3 3
4 39
5 4
6 4
7 4
8 5
9 6
10 5
11 5
12 6
13 5
14 5
15 5
16 7
17 6
18 6
19 11
20 7
21 6
22 29
23 6
24 6
25 7
26 6
27 6
28 7
29 6
30 6
31 6
32 8
33 8
34 7
35 7
36 10
37 9
38 7
39 8
40 9
41 7
42 8
43 7
44 7
45 8
46 7
47 8
48 10
49 7
50 7
51 26
52 9
53 7
54 8
55 7
56 7
57 10
58 7
59 7
60 8
61 7
62 7
63 7
64 47
65 8
66 14
67 9
68 11
69 10
70 9
71 10
72 8
73 9
74 8
75 8
76 31
77 8
78 8
79 15
80 8
81 10
82 9
83 9
84 8
85 11
86 10
87 8
88 9
89 8
90 12
91 9
92 8
93 8
94 11
95 8
96 14
97 21
98 8
99 8