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A261905 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). 0

%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

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Last modified March 30 04:37 EDT 2024. Contains 371289 sequences. (Running on oeis4.)