A256944 Squares which are not the sums of two consecutive nonsquares.

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

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

a(n) = A257282(n)^2. - M. F. Hasler, May 08 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