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A139476
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Positions of squares in the EKG sequence (A064413).
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7
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1, 3, 6, 17, 24, 30, 50, 64, 76, 86, 124, 136, 171, 180, 209, 240, 290, 303, 359, 385, 417, 436, 521, 547, 595, 643, 696, 747, 823, 850, 947, 982, 1022, 1102, 1171, 1234, 1313, 1381, 1453, 1525, 1642, 1688, 1810, 1855, 1931, 2033, 2168, 2203
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OFFSET
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1,2
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COMMENTS
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Conjecture: the squares appear in increasing order.
It appears after inspecting 40000 terms that all the n-th powers (squares, cubes, etc.) appear in increasing order. - Jacques Tramu, May 10 2008
The conjecture is false; in the EKG sequence, 158^2 is at position 24142, but 157^2 is at position 24146. Note that 157 is prime. If we let p=157, then the two terms on either side of p^2 are p(p+2) and p(p+3), which is unusual because for all primes 3 < p < 157, the three terms are p(p+1), p^2, p(p+2). The next unusual prime is 661. There are no others less than 8164.
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LINKS
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EXAMPLE
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The position of 2^2 = 4 is 3 - the second term in the sequence.
The position of 3^2 = 9 is 6 - the third term in the sequence.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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