This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A377305 #36 Nov 17 2024 07:06:00 %S A377305 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, %T A377305 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, %U A377305 3,2,4,5,6,9,7,6,8,10,12,11,11,9,12,12,13,11,14,13 %N A377305 Number of times A278603(n) has occurred among the terms of that sequence so far, i.e. among A278603(0..n). %e A377305 Among the terms of A278603 the value of A278603(14) = 4 occurs 3 times, counting as far as n = 14: %e A377305 . %e A377305 n: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... %e A377305 ------------------------------------------------------------------------------ %e A377305 A278603(n): 0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 7, 6, 5, ... %e A377305 ------------------------------------------------------------------------------ %e A377305 * * * %e A377305 Count: 1 2 3 -> therefore a(14) = 3. %e A377305 . %e A377305 The counting of equal altitude points is also explained with this diagram. %e A377305 Up to and including A278603(14) = 4, climbing from origin, we touch 3 equal altitude %e A377305 points at height 4 on the mountain at A278603(10) = 4, A278603(12) = 4, and A278603(14) = 4. %e A377305 . %e A377305 Altitude 4 /\ %e A377305 touched / \... %e A377305 3 times _________/\__/ %e A377305 reaching / \/ %e A377305 n = 14 /\ / %e A377305 /\/ \/ %e A377305 / %e A377305 . %e A377305 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: %e A377305 . %e A377305 Al-| %e A377305 ti-| - a(n) - %e A377305 tu-| %e A377305 de | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... %e A377305 ------------------------------------------------------------------------------------ %e A377305 . | ... %e A377305 28 | 186 ... %e A377305 27 | 157 185 ... %e A377305 26 | 156 158 184 ... %e A377305 25 | 155 159 167 179 183 ... %e A377305 24 | 154 160 166 168 178 180 182 ... %e A377305 23 | 149 153 161 165 169 177 181 ... %e A377305 22 | 148 150 152 162 164 170 176 ... %e A377305 21 | 147 151 163 171 175 ... %e A377305 20 | 146 172 174 ... %e A377305 19 | 145 173 ... %e A377305 18 | 144 ... %e A377305 17 | 143 ... %e A377305 16 | 142 ... %e A377305 15 | 137 141 ... %e A377305 14 | 136 138 140 ... %e A377305 13 | 127 135 139 ... %e A377305 12 | 126 128 134 ... %e A377305 11 | 125 129 133 ... %e A377305 10 | 124 130 132 ... %e A377305 9 | 23 67 123 131 ... %e A377305 8 | 22 24 66 68 122 ... %e A377305 7 | 17 21 25 65 69 73 97 121 ... %e A377305 6 | 16 18 20 26 64 70 72 74 96 98 120 ... %e A377305 5 | 11 15 19 27 31 47 59 63 71 75 83 95 99 103 119 ... %e A377305 4 | 10 12 14 28 30 32 46 48 58 60 62 76 82 84 94 100 102 104 118 ... %e A377305 3 | 5 9 13 29 33 41 45 49 57 61 77 81 85 93 101 105 109 117 ... %e A377305 2 | 2 4 6 8 34 40 42 44 50 56 78 80 86 92 106 108 110 116 ... %e A377305 1 | 1 3 7 35 39 43 51 55 79 87 91 107 111 115 ... %e A377305 0 | 0 36 38 52 54 88 90 112 114 ... %e A377305 -1 | 37 53 89 113 ... %e A377305 . | ... %e A377305 . %Y A377305 Cf. A278603. %K A377305 nonn %O A377305 0,4 %A A377305 _Tamas Sandor Nagy_, Oct 23 2024