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A383595 a(n) is the smallest prime k such that (prime(n), k, u, v) are the vertices of a square in Ulam's spiral, where k < u < v are all primes; or -1 if there is no such k.

Table of values

n a(n)
1 -1
2 -1
3 -1
4 56527
5 59
6 67
7 251
8 -1
9 -1
10 2473
11 3001
12 43
13 43
14 41
15 173
16 1621
17 61
18 59
19 13
20 141937
21 13
22 13
23 10459
24 331
25 33211
26 643
27 179
28 41
29 41
30 1429
31 11
32 11
33 59
34 59
35 13
36 127
37 163
38 157
39 169957
40 47
41 103
42 56519
43 683
44 2843
45 6841
46 211
47 199
48 311
49 59407
50 439
51 11
52 137
53 274831

List of values

[-1, -1, -1, 56527, 59, 67, 251, -1, -1, 2473, 3001, 43, 43, 41, 173, 1621, 61, 59, 13, 141937, 13, 13, 10459, 331, 33211, 643, 179, 41, 41, 1429, 11, 11, 59, 59, 13, 127, 163, 157, 169957, 47, 103, 56519, 683, 2843, 6841, 211, 199, 311, 59407, 439, 11, 137, 274831]