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).

1, 2, 5, 6, 8, 9, 11, 14, 17, 19, 22, 24, 29, 34, 41

Offset

1,2

Comments

Cauchy showed that this list is complete [see Dickson].

References

L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea NY 1992, see pages 18 and 284.

Links

Table of n, a(n) for n=1..15.

Maple

# Maple program that verifies that there are no other terms below 100
ans:=[]; for n from 1 to 100 do
t1:=ceil(sqrt(3*n)); t2:=floor(sqrt(4*n)); sw:=1;
   for i from t1 to t2 do if n-i mod 2 = 0 then sw:=-1; fi; od:
if sw=1 then ans:=[op(ans), n]; fi; od:
ans;

Crossrefs

Sequence in context: A049636 A045573 A161152 * A340602 A350945 A273867

Adjacent sequences: A261902 A261903 A261904 * A261906 A261907 A261908

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Sep 09 2015

Status

approved