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Search: id:A108269
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| A108269 |
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Numbers of the form a(m, n) = (2m - 1)*4^n where m >= 1, n >= 1. |
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+0
2
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| 4, 12, 16, 20, 28, 36, 44, 48, 52, 60, 64, 68, 76, 80, 84, 92, 100, 108, 112, 116, 124, 132, 140, 144, 148, 156, 164, 172, 176, 180, 188, 192, 196, 204, 208, 212, 220, 228, 236, 240
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OFFSET
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1,1
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COMMENT
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Numbers of terms in nonnegative integer sequences the sum of which is not a square.
The sum of a sequence of consecutive nonnegative integers starting with k is never a square for any k, if and only if the number of the terms in the sequence can be expressed as ( 2m - 1 ) * 2^( 2n ), m and n being any positive integers. (Proved by Alfred Vella, Jun 14 2005.)
Odious and evil terms alternate. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 22 2009]
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EXAMPLE
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a( 1, 1 ) = 4, a( 2, 1) = 12, etc
For a( 1, 1 ): the sum of 4 consecutive nonnegative integers (4k+6, if the first term is k) is never a square.
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CROSSREFS
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Sequence in context: A082420 A053362 A077770 this_sequence A081523 A053006 A057962
Adjacent sequences: A108266 A108267 A108268 this_sequence A108270 A108271 A108272
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KEYWORD
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nonn
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AUTHOR
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Andras Erszegi (erszegi.andras(AT)chello.hu), May 30 2005
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jun 26 2005
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