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%I #21 Oct 30 2013 05:34:55
%S 0,1,2,3,4,5,6,7,9,11,12,13,16,17,19,20,23,25,29,30,31,36,37,41,42,43,
%T 47,49,53,56,59,61,64,67,71,72,73,79,81,83,89,90,97,100,101,103,107,
%U 109,110,113,121,127,131,132,137,139,144,149,151,156,157,163,167,169
%N Primes and quarter-squares.
%C Union of A002620 and A000040.
%C It appears that there is always a prime between two consecutive quarter squares, if n >= 2. Therefore in a square spiral, or zig-zag, whose vertices are the quarter-squares, it appears that there is always a prime between two consecutive vertices, if n >= 2.
%C Apparently the above comment is equivalent to the Oppermann's conjecture. - _Omar E. Pol_, Oct 26 2013
%C Union of A000040 and A000290 and A002378. - _Omar E. Pol_, Oct 28 2013
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Oppermann's_conjecture">Oppermann's conjecture</a>
%F a(n) ~ n log n. - _Charles R Greathouse IV_, Mar 04 2013
%t mx = 13; Union[Prime[Range[PrimePi[mx^2]]], Floor[Range[2*mx]^2/4]] (* _Alonso del Arte_, Mar 03 2013 *)
%Y Cf. A000040, A002620, A000290, A014085, A220492, A220506, A220508, A220516.
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Feb 05 2013
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