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A111693
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a(n) = nextprime((2*n-1)^2) for n >= 2, a(1) = 3.
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0
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3, 11, 29, 53, 83, 127, 173, 227, 293, 367, 443, 541, 631, 733, 853, 967, 1091, 1229, 1373, 1523, 1693, 1861, 2027, 2213, 2411, 2609, 2819, 3037, 3251, 3491, 3727, 3989, 4229, 4493, 4783, 5051, 5333, 5639, 5939, 6247, 6563, 6899, 7229, 7573, 7927, 8287, 8663
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OFFSET
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1,1
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COMMENTS
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Old name was: The number system may be represented by linearly stringing together all the square domains. The number of the domain is given by r. It is noted that this has the same value as the circuit number in the Ellerstein square spiral. One below each odd square is a zero-centered octagonal number, which is divisible by 8. The value of this is eight times a triangular number. It may be seen that there are r octads in each square domain. The sequence is the first prime number in the first octad of each square domain.
It is noted that each square domain has 8 sectors of length r besides the r octads of length 8 which are intertwined.
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REFERENCES
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Stuart M. Ellerstein, The Pronic Renaissance: The Ulam Square Spiral (Modified), J. Recreational Mathematics, Vol. 29, 3, pp. 188-189, 1998.
Stuart M. Ellerstein, The Pronic Renaissance II: The Ellerstein Square Spiral, J. Recreational Mathematics, Vol. 30, 4, pp. 246-250, 1999-2000.
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LINKS
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FORMULA
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EXAMPLE
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For the sixth square domain, r=6. The ZCON is 120, which is 8*15, since it is 8*6(6-1)/2 and the first prime is 8*15 + 7. The odd square is (2r -1)^2 = 121.
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MAPLE
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a:= n-> `if`(n=1, 3, nextprime((2*n-1)^2)):
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), Jun 17 2006
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EXTENSIONS
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STATUS
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approved
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