A166264 If the n-th prime is denoted by p(n) then a(j) = frequency with which each distinct value of (Sum of the quadratic non-residues of p(n) - Sum of the quadratic residues of p(n)) / p(n) occurs.

174195, 6, 16, 25, 31, 34, 41, 37, 68, 45, 47, 85, 68, 95, 93, 83, 73, 101, 103, 85, 115, 109, 106, 154, 107, 132, 159, 114, 163, 179, 128, 132, 216, 164, 120, 209, 150, 119, 237, 216, 175, 228, 150, 221, 222, 192, 214, 262, 241, 185, 289, 196, 181, 379, 189

Offset: 1

Author

Christopher Hunt Gribble, Oct 10 2009

Keywords

• nonn

Comments

The table below shows a(j) for each distinct value of (Sum of the quadratic non-residues of p(n) - Sum of the quadratic residues of p(n)) / p(n) for 1 <= n <= 348513, with p(348513) = 4999999 (< 5*10^6).

a(1) appears to increase indefinitely, so the static sequence starts at a(2).

j (SQN-SQR)/p(n) a(j)

-- -------------- ------

1 0 174195

2 1 6

3 3 16

4 5 25

5 7 31

6 9 34

7 11 41

8 13 37

9 15 68

10 17 45

11 19 47

12 21 85

13 23 68

14 25 95

15 27 93

16 29 83

17 31 73

18 33 101

19 35 103

20 37 85

21 39 115

22 41 109

23 43 106

24 45 154

25 47 107

26 49 132

27 51 159

28 53 114

29 55 163

30 57 179

31 59 128

32 61 132

33 63 216

34 65 164

35 67 120

36 69 209

37 71 150

38 73 119

39 75 237

40 77 216

41 79 175

42 81 228

43 83 150

44 85 221

45 87 222

46 89 192

47 91 214

48 93 262

49 95 241

50 97 185

51 99 289

52 101 196

53 103 181

54 105 379

55 107 189

56 109 209

57 111 314

58 113 239

Links

• Christopher Hunt Gribble, Table of n, a(n) for n = 1..1973.

Crossrefs

Cf. A165951, A165974, A004273.