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A063951
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Every number is the sum of 4 squares; these are the odd numbers n such that the first square can be taken to be any positive square < n.
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3
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1, 3, 5, 7, 9, 13, 15, 17, 21, 25, 33, 41, 45, 49, 57, 65, 73, 81, 89, 97, 105, 129, 145, 153, 169, 177, 185, 201, 209, 217, 225, 257, 273, 297, 305, 313, 329, 345, 353, 385, 425, 433, 441, 481, 513, 561, 585, 609, 689, 697, 713, 817, 825, 945
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OFFSET
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1,2
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COMMENTS
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Odd numbers n such that for all k with 1 <= k < sqrt(n), n - k^2 is not in A004215. - Robert Israel, Jan 24 2018
The only numbers for which allowing k = 0 would make a difference are 7 and 15: These two are not in A063954.
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REFERENCES
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J. H. Conway, personal communication, Aug 27, 2001.
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LINKS
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FORMULA
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MAPLE
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isA004215:= proc(n)
local t;
t:= padic:-ordp(n, 2);
t::even and (n/2^t) mod 8 = 7
end proc:
filter:= proc(n) andmap(not(isA004215), [seq(n - k^2, k=1..floor(sqrt(n-1)))]) end proc:
select(filter, [seq(i, i=1..1000, 2)]); # Robert Israel, Jan 24 2018
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MATHEMATICA
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ok[n_] := Range[ Floor[ Sqrt[n] ]] == DeleteCases[ Union[ Flatten[ PowersRepresentations[n, 4, 2]]], 0, 1, 1]; A063951 = Select[ Range[1, 999, 2], ok] (* Jean-François Alcover, Sep 12 2012 *)
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PROG
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(PARI) is_A063951(n)=bittest(n, 0)&&!forstep(k=sqrtint(n-1), 1, -1, isA004215(n-k^2)&&return) \\ M. F. Hasler, Jan 26 2018
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CROSSREFS
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KEYWORD
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nonn,easy,nice,fini,full
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AUTHOR
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STATUS
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approved
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