A020497

[David W. Wilson]

Per recent discussions of pi(x)+pi(y) < pi(x+y) and admissible
constellations, let c(n) be the maximum size of an admissible
constellation on an interval of n integers (c(n) = A023193(n)).  Then
A020497(n) purportedly gives the least k with c(k) = n, that is,
A020497 should be the "least inverse" of A023193.

A020497 as it stands (indexed starting at 1) is:

1 3 7 9 13 17 21 27 31 33 37 43 49 51 57 61 67 71 77 87 85 97 95 103
111 117 121 129 133 139 141 147 153 157 159 163 169 177

Whereas I compute:

1 3 7 9 13 17 21 27 31 33 37 43 49 51 57 61 67 71 77 81 85 91 95 101
111 115 121 127 131 137 141 147 153 157 159 163 169 177 183 187 189 197
201 211 213 217 227 237 241 247 253 255 265 271 273 279 283 289 301 305

The discrepancies are summarized below:

               n      A020497(n)         my a(n)
              ----------------------------------
              20              87              81
              22              97              91
              24             103             101
              26             117             115
              28             129             127
              29             133             131
              30             139             137

The first two discrepancies appear to be typos (writing 7 for 1),
while the others may be honest inaccuracies.  At any rate, my
computed value is in every case smaller than the published value.
Thus, in each case, I can defend my value by exhibiting an
admissible constellation of n elements on the range [1, a(n)].

Constellation for a(20) = 81:
(1 3 7 9 13 21 27 31 37 39 43 49 51 57 63 67 69 73 79 81)

Constellation for a(22) = 91:
(1 5 11 13 19 23 25 29 35 41 43 49 53 55 61 65 71 79 83 85 89 91)

Constellation for a(24) = 101:
(1 5 7 11 17 19 25 29 31 35 41 47 49 55 59 61 67 71 77 85 89 95 97 101)

Constellation for a(26) = 115:
(1 5 7 11 13 17 25 31 35 41 43 47 53 61 67 71 73 77 83 85 91 95 97 101
113 115)

Constellation for a(28) = 127:
(1 5 7 17 19 29 31 35 37 41 47 49 55 59 61 71 79 85 89 91 97 101 107
115 119 121 125 127)

Constellation for a(29) = 131:
(1 5 7 11 17 19 29 31 35 37 49 59 61 65 67 71 77 79 85 89 95 101 107
109 115 119 121 127 131)

Constellation for a(30) = 137:
(1 5 7 11 17 19 29 31 35 37 49 59 61 65 67 71 77 79 85 89 95 101 107
109 115 119 121 127 131 137)

Can someone verify that these constellations are indeed admissible?
Then NJAS can confidently update A020497.