A063951 - OEIS

%I #27 Jan 30 2018 21:10:47

%S 1,3,5,7,9,13,15,17,21,25,33,41,45,49,57,65,73,81,89,97,105,129,145,

%T 153,169,177,185,201,209,217,225,257,273,297,305,313,329,345,353,385,

%U 425,433,441,481,513,561,585,609,689,697,713,817,825,945

%N 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.

%C 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

%C The only numbers for which allowing k = 0 would make a difference are 7 and 15: These two are not in A063954.

%D J. H. Conway, personal communication, Aug 27, 2001.

%F This A063951 = A063954 U { 7, 15 }. - _M. F. Hasler_, Jan 27 2018

%p isA004215:= proc(n)

%p   local t;

%p   t:= padic:-ordp(n,2);

%p   t::even and (n/2^t) mod 8 = 7

%p end proc:

%p filter:= proc(n) andmap(not(isA004215), [seq(n - k^2, k=1..floor(sqrt(n-1)))]) end proc:

%p select(filter, [seq(i,i=1..1000,2)]); # _Robert Israel_, Jan 24 2018

%t 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 *)

%o (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

%o (PARI) A063951=select(is_A063951,[1..945]) \\ _M. F. Hasler_, Jan 26 2018

%Y Cf. A004215, A063949, A063950, A063952, A063953, A063954.

%K nonn,easy,nice,fini,full

%O 1,2

%A _N. J. A. Sloane_, Sep 04 2001