A377305 Number of times A278603(n) has occurred among the terms of that sequence so far, i.e. among A278603(0..n).

1, 1, 1, 2, 2, 1, 3, 3, 4, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 4, 4, 4, 5, 5, 6, 5, 5, 4, 2, 1, 3, 5, 6, 6, 7, 6, 8, 7, 7, 6, 8, 8, 9, 7, 4, 2, 5, 8, 10, 9, 9, 7, 10, 10, 11, 8, 5, 4, 3, 2, 4, 5, 6, 9, 7, 6, 8, 10, 12, 11, 11, 9, 12, 12, 13, 11, 14, 13

Offset

0,4

Links

Table of n, a(n) for n=0..85.

Example

Among the terms of A278603 the value of A278603(14) = 4 occurs 3 times, counting as far as n = 14:
.
           n:  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19  ...
 ------------------------------------------------------------------------------
  A278603(n):  0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 7, 6, 5, ...
 ------------------------------------------------------------------------------
                                             *     *     *
       Count:                                1     2     3  -> therefore a(14) = 3.
.
The counting of equal altitude points is also explained with this diagram.
Up to and including A278603(14) = 4, climbing from origin, we touch 3 equal altitude
points at height 4 on the mountain at A278603(10) = 4, A278603(12) = 4, and A278603(14) = 4.
.
  Altitude 4              /\
  touched                /  \...
  3 times  _________/\__/
  reaching         /  \/
  n = 14      /\  /
           /\/  \/
          /
.
An array as a histogram that shows in rows the equal altitude points on the prime mountain, stacked into columns. The prime mountain is squashed horizontally like a concertina to bring its equal altitude points close together, left-justified, and so to create a compact visual form for analysis. The number of equal altitude points, a(n), so far as n, can be read from the column headings, here in the range of n = 0, ..., 186:
.
 Al-|
 ti-|                                 - a(n) -
 tu-|
 de |  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  ...
 ------------------------------------------------------------------------------------
  . | ...
 28 | 186 ...
 27 | 157 185 ...
 26 | 156 158 184 ...
 25 | 155 159 167 179 183 ...
 24 | 154 160 166 168 178 180 182 ...
 23 | 149 153 161 165 169 177 181 ...
 22 | 148 150 152 162 164 170 176 ...
 21 | 147 151 163 171 175 ...
 20 | 146 172 174 ...
 19 | 145 173 ...
 18 | 144 ...
 17 | 143 ...
 16 | 142 ...
 15 | 137 141 ...
 14 | 136 138 140 ...
 13 | 127 135 139 ...
 12 | 126 128 134 ...
 11 | 125 129 133 ...
 10 | 124 130 132 ...
  9 |  23  67 123 131 ...
  8 |  22  24  66  68 122 ...
  7 |  17  21  25  65  69  73  97 121 ...
  6 |  16  18  20  26  64  70  72  74  96  98 120 ...
  5 |  11  15  19  27  31  47  59  63  71  75  83  95  99 103 119 ...
  4 |  10  12  14  28  30  32  46  48  58  60  62  76  82  84  94 100 102 104 118 ...
  3 |   5   9  13  29  33  41  45  49  57  61  77  81  85  93 101 105 109 117 ...
  2 |   2   4   6   8  34  40  42  44  50  56  78  80  86  92 106 108 110 116 ...
  1 |   1   3   7  35  39  43  51  55  79  87  91 107 111 115 ...
  0 |   0  36  38  52  54  88  90 112 114 ...
 -1 |  37  53  89 113 ...
  . | ...
.

Crossrefs

Cf. A278603.

Sequence in context: A191521 A245370 A321341 * A284549 A200779 A286558

Adjacent sequences: A377302 A377303 A377304 * A377306 A377307 A377308

Keyword

nonn

Author

Tamas Sandor Nagy, Oct 23 2024

Status

approved