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Search: id:A111302
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| A111302 |
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Define a(1)=1. Thereafter a(n) is the smallest positive integer with the property that a(n)^2 cannot be created by summing the squares of at most n values chosen among the previous terms (with repeats allowed). |
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+0
1
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| 1, 2, 4, 9, 12, 16, 27, 49, 69, 118, 187, 305, 503, 829, 1590, 2529, 4173, 7189, 13771, 22854, 43460, 57549, 135271, 222070, 426775, 724479, 1246636, 2158543, 3713979, 6063658, 11725956, 19627746
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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No more terms < 22155000. [From David Wasserman (dwasserm(AT)earthlink.net), Jan 09 2009]
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EXAMPLE
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a(3) <> 3 because we can write 3^2=a(2)^2+a(2)^2+a(1)^2 by using not more than 3 terms.
But it is impossbile to write 4^2 as the sum of at most three squares of the previous elements, thus a(3)=4.
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PROGRAM
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Contribution from David Wasserman (dwasserm(AT)earthlink.net), Jan 09 2009: (Start)
(PARI) canMake(n, v, i, left) = local(c); if (i == 0, return(n <= left)); c = v[i]; if (n > left*c, return(0)); if (!(n%c), return(1)); forstep (j = n\c, 0, -1, if (canMake(n - j*c, v, i - 1, left - j), return(1))); 0;
v = vector(60); x = 2; for (m = 2, 61, while (canMake(x^2, v, m - 2, m), x++); v[m - 1] = x^2; print(x); x++); (End)
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CROSSREFS
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Sequence in context: A022428 A096186 A088901 this_sequence A092530 A154891 A139557
Adjacent sequences: A111299 A111300 A111301 this_sequence A111303 A111304 A111305
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KEYWORD
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nonn,hard
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AUTHOR
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Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 02 2005
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EXTENSIONS
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More terms from David Wasserman (dwasserm(AT)earthlink.net), Jan 09 2009
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