A363665 Starting with a(1) = 1, the lexicographically earliest sequence of integers on a square spiral such that every number equals the sum of its eight adjacent neighbors.
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, -2, 0, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, -1, 2, -3, 0, 0, 3, -2, 2, -3, 0, 0, 3, -1, -1, 1, 0, 0, 1, 0, 0, -5, 8, 0, 0, -5, 4, 0, 4, -7, 0, 0, 6, -6, 4, -4, 8, -7, 0, 0, 2, -2, 4, -4, 0, 7, 0, 0, -8, 6, 3, -8, 10, -15, 16, 0, 0, -9, 6, -5, 7, -8, 13
Offset: 1
Keywords
Examples
The spiral begins:
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0__-3___2__-2___3___0___0 -7
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0 0__-2___1___0___0 -3 4
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3 0 0___0___0 -2 2 0
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-1 0 0 1___0 0 -1 4
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-1 -1 0___0___1___0 0 -5
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1 0___0___0__-2___2___0 0
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0___0___1___0___0__-5___8___0
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a(9) = 1 as a(1) = 1 and a(2)..a(8) = 0, therefore a(9) = 1 so the sum of the eight numbers around a(1) equals 1.
a(12) = -2 as a(2) = 0 while a(1), a(9) = 1, a(2)..a(4), a(8), a(10), a(11) = 0, therefore a(12) = -2 so the sum of the eight numbers around a(1) equals 0.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..10000.
- Scott R. Shannon, Image of log_10(a(n)+1) of the absolute value of the first 500000 terms.
- Scott R. Shannon, Image showing the sign of the first 500000 terms on the spiral. White is positive, black is negative, yellow is zero.
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