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 A256944 Squares which are not the sums of two consecutive nonsquares. 4
 0, 1, 4, 9, 16, 36, 49, 64, 100, 144, 196, 256, 289, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1681, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100, 8464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The union of A008843, A055792, and A016742. [Corrected by Charles R Greathouse IV, May 07 2015] Consists of the squares of all even numbers and odd numbers in A078057 = (1, 3, 7, 17, 41, 99, ...), see also A001333 = abs(A123335). See A257282 for the square roots and A257292 for their complement in the nonnegative integers A001477. - M. F. Hasler, May 08 2015 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 FORMULA a(n) ~ 4n^2. - Charles R Greathouse IV, May 07 2015 EXAMPLE 0, 1, 4, 9, 16, 36, are in this sequence because first 14 sums of two consecutive nonsquares are 5, 8, 11, 13, 15, 18, 21, 23, 25, 27, 29, 32, 35, 37. MATHEMATICA lim = 15000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Range@ Floor[Sqrt[lim]]^2, !MemberQ[s, #] &] (* Michael De Vlieger, Apr 29 2015 *) lst=Partition[Select[Range[0, 10^6], !IntegerQ[Sqrt[#]]&], 2, 1]/.{a_, b_}->  a+b; a256944=Complement[Table[n^2, {n, 0, Sqrt[Last[lst]]}], lst] (* timing improved by Ivan N. Ianakiev, Apr 30 2015 *) Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 6]]^2 (* Michael De Vlieger, Aug 06 2016, after Harvey P. Dale at A001333 *) PROG (PARI) is(n)=issquare(n) && (n%2==0 || issquare(n\2) || issquare(n\2+1)) \\ Charles R Greathouse IV, May 07 2015 CROSSREFS Cf. A000037, A000290, A008843, A016742, A056792, A257282. Sequence in context: A100498 A068952 A000548 * A349062 A106575 A025620 Adjacent sequences:  A256941 A256942 A256943 * A256945 A256946 A256947 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Apr 25 2015 STATUS approved

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)