Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Aug 23 2023 08:37:30
%S 1,2,5,6,8,9,11,14,17,19,22,24,29,34,41
%N Numbers m with the property that there is no number k in the range ceiling(sqrt(3m)) <= k <= floor(sqrt(4m)) with k == m (mod 2).
%C Cauchy showed that this list is complete [see Dickson].
%D L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea NY 1992, see pages 18 and 284.
%p # Maple program that verifies that there are no other terms below 100
%p ans:=[]; for n from 1 to 100 do
%p t1:=ceil(sqrt(3*n)); t2:=floor(sqrt(4*n)); sw:=1;
%p for i from t1 to t2 do if n-i mod 2 = 0 then sw:=-1; fi; od:
%p if sw=1 then ans:=[op(ans),n]; fi; od:
%p ans;
%K nonn,fini,full
%O 1,2
%A _N. J. A. Sloane_, Sep 09 2015