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A257282
Numbers whose square is not the sum of two consecutive nonsquares.
4
0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 14, 16, 17, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 41, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 106, 108, 110, 112, 114, 116
OFFSET
1,3
COMMENTS
See A256944 for further information.
Union of even integers and A001333. - Ivan Neretin, Aug 04 2016
LINKS
FORMULA
a(n) = sqrt(A256944).
a(n) ~ 2n. [Following Charles R Greathouse IV's formula for A256944.]
EXAMPLE
5 is not in the sequence because 5^2 = 25 = 12 + 13 is the sum of two consecutive numbers both of which are not squares.
All even numbers are in the sequence because (2k)^2 = 4k^2 cannot be written as sum of two consecutive numbers and 2k^2 is not a square.
An odd number n is in the sequence if one of the two numbers next to n^2/2 is a square.
MATHEMATICA
Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 7]] (* Michael De Vlieger, Aug 06 2016, after Harvey P. Dale at A001333 *)
PROG
(PARI) is(n)={n%2==0 || issquare(n^2\2) || issquare(n^2\2+1)}
CROSSREFS
Cf. A256944.
Sequence in context: A225620 A335041 A335042 * A336488 A221178 A080389
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, May 08 2015
STATUS
approved