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A308505
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Counterclockwise square spiral of distinct positive integers constructed by greedy algorithm, such that for p = 2 and 3, every multiple of p (except p itself) is vertically or horizontally adjacent to a cell already holding a multiple of p.
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2
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1, 2, 3, 5, 7, 11, 13, 17, 4, 8, 10, 6, 9, 15, 19, 23, 25, 29, 31, 35, 37, 41, 43, 14, 16, 20, 22, 26, 12, 18, 21, 27, 33, 39, 45, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 77, 28, 32, 34, 38, 40, 44, 46, 24, 30, 36, 42, 48, 50, 51, 57, 63, 69, 75, 79, 83, 85
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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For p = 2 and 3, the set S_p of lattice points holding a multiple of p is connected with respect to von Neumann neighborhood and has interesting graphical features (see representation in Links section).
Apparently this sequence is a permutation of the natural number with infinitely many fixed points.
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LINKS
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Table of n, a(n) for n=1..67.
Rémy Sigrist, Representation of S_2 restricted to -500 <= x <= +500 and -500 <= y <= +500
Rémy Sigrist, Representation of S_3 restricted to -500 <= x <= +500 and -500 <= y <= +500
Rémy Sigrist, Colored representation of (a(n)-n) restricted to -500 <= x <= +500 and -500 <= y <= +500 (where black pixels correspond to zeros, blue shades correspond to negative values and red shades correspond to positive values)
Rémy Sigrist, PARI program for A308505
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EXAMPLE
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The spiral begins:
111--105---99---93---87---86---84---82---81---80---78
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117 79---75---69---63---57---51---50---48---42 72
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119 83 49---47---45---39---33---27---21 36 66
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121 85 53 25---23---19---15----9 18 30 60
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125 89 55 29 7----5----3 6 12 24 54
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127 91 59 31 11 1----2 10 26 46 76
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131 95 61 35 13---17----4----8 22 44 74
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133 97 65 37---41---43---14---16---20 40 70
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137 101 67---71---73---77---28---32---34---38 68
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139 103--107--109--113--115---52---56---58---62---64
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143--145--149--151--155--157---88---92---94---98--100
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PROG
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(PARI) See Links section.
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CROSSREFS
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Cf. A005843, A008585.
Sequence in context: A020625 A033633 A242119 * A338938 A249823 A171049
Adjacent sequences: A308502 A308503 A308504 * A308506 A308507 A308508
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KEYWORD
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nonn
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AUTHOR
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Rémy Sigrist, Jun 02 2019
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STATUS
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approved
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