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Search: id:A076114
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| A076114 |
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a(n) = start of the smallest string of n consecutive positive integers with a square sum, or 0 if no such number exists. |
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+0
3
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| 1, 4, 2, 0, 3, 11, 4, 1, 5, 18, 6, 0, 7, 25, 8, 0, 9, 4, 10, 0, 11, 39, 12, 2, 4, 46, 14, 0, 15, 53, 16, 9, 17, 60, 18, 0, 19, 67, 20, 3, 21, 74, 22, 0, 23, 81, 24, 0, 1, 16, 26, 0, 27, 11, 28, 4, 29, 102, 30, 0, 31, 109, 32, 0, 33, 116, 34, 0, 35, 123, 36, 5, 37, 130, 11, 0, 39
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equivalently, smallest k such that n(n+2k-1)/2 is a square, 0 if there is no such square. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 23 2003
a(n)=0 if and only if n has the form 4^e*m with e>0 and m odd. - Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 25 2003
a(k) = 1 if k is the index of a square triangular number, i.e. k(k+1)/2 is a square or if k belongs to A001108. If n is odd then a(n) <= (n+1)/2.
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EXAMPLE
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a(2) = 4, 4+5 = 9= 3^2. a(8) = 1, 1+2+3+4+5+6+7+8 = 36 = 6^2.
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PROGRAM
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(PARI) for(n=1, 100, o=n*(n+1)/2:k=0:while(k<10^5&&!issquare(o+n*k), k=k+1): if(k>=10^5, k=-1):print1(k+1", "))
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CROSSREFS
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Cf. A001108, A001109, A076115.
Sequence in context: A106220 A104689 A048819 this_sequence A051478 A121829 A021708
Adjacent sequences: A076111 A076112 A076113 this_sequence A076115 A076116 A076117
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Oct 09 2002
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EXTENSIONS
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More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 23 2003
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