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A062316 Neither the sum or difference of 2 squares.

%I A062316 #28 Jan 08 2019 09:12:41
%S A062316 6,14,22,30,38,42,46,54,62,66,70,78,86,94,102,110,114,118,126,134,138,
%T A062316 142,150,154,158,166,174,182,186,190,198,206,210,214,222,230,238,246,
%U A062316 254,258,262,266,270,278,282,286,294,302,310,318,322,326,330,334,342,350,354,358
%N A062316 Neither the sum or difference of 2 squares.
%C A062316 Elements of A022544 congruent to 2 (mod 4).
%C A062316 Union of numbers congruent to 6 mod 8 (A017137) with numbers of the form 2 * A084109(n). - _Franklin T. Adams-Watters_, Jan 21 2007
%C A062316 Explanation: odd numbers are equal to the difference between two successive squares and among even numbers, multiples of 4 are of the form (k+2)^2-k^2, thus odd numbers and multiples of 4 are not in the sequence. Conversely, a difference of 2 squares cannot equal 2 (mod 4), thus this sequence contains the integers of the form 4k+2 that are in A022544 (not the sum of two squares); among integers of form 4k+2, this sequence contains all the integers of the form 8n+6 (A017137) that are not the sum of 2 squares because they have at least one prime factor congruent to 3 (mod 4) to an odd power; it also contains integers of the form 8n+2 = 2(4n+1) with 4n+1 not the sum of two squares, which is sequence A084109. - _Jean-Christophe Hervé_, Oct 24 2015
%H A062316 Jean-Christophe Hervé, <a href="/A062316/b062316.txt">Table of n, a(n) for n = 1..2507</a>
%F A062316 a(n) == 2 (mod 4). Subsequence of A016825 (non-differences of squares). All first differences are either 4 or 8, each of which occurs infinitely often. - _David W. Wilson_, Mar 09 2005
%F A062316 Lim_{n->inf} a(n)/n = 4.
%e A062316 From _Jean-Christophe Hervé_, Oct 24 2015: (Start)
%e A062316 6, 14, 22, 30, 38, 46, ... are in the sequence because they equal 6 (mod 8).
%e A062316 42 = 2*3*7, 66 = 2*3*11, 114 = 2*7*11 are also in the sequence: of the form 2*(4n+1) with 4n+1 not the sum of 2 squares.
%e A062316 (End)
%p A062316 N:= 1000: # to get all terms <= N
%p A062316 S:= {seq(4*i+2,i=0..floor((N-2)/4))}
%p A062316   minus {seq(seq(x^2 + y^2, y = x .. floor(sqrt(N-x^2)),2),x=1..floor(sqrt(N)))}:
%p A062316 sort(convert(S,list)); # _Robert Israel_, Oct 25 2015
%t A062316 Select[Range@ 360, SquaresR[2, #] == 0 && Mod[#, 4] == 2 &] (* _Michael De Vlieger_, Oct 26 2015, after _Harvey P. Dale_ at A022544 *)
%Y A062316 Cf. A022544, A016825, union of A017137 and 2*A084109, complement of A263715.
%Y A062316 Cf. A097271, A079299.
%K A062316 nonn
%O A062316 1,1
%A A062316 _Michel ten Voorde_, Jul 05 2001
%E A062316 More terms from _David W. Wilson_, Feb 11 2003