Search: id:A077767
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%I A077767
%S A077767 1,1,1,2,1,2,1,3,1,2,3,3,2,3,3,3,2,3,3,3,4,5,3,4,4,4,3,5,4,4,5,5,4,4,5,
%T A077767 5,4,8,8,5,4,6,5,6,7,5,5,7,5,7,7,7,6,8,4,5,11,5,9,8,6,11,7,7,7,7,8,10,
%U A077767 5,12,10,5,9,10,7,13,8,8,11,5,10,9,13,9,6,9,12,7,7,11,10,9,12,11,10,10
%N A077767 Number of primes of form 4k+3 between n^2 and (n+1)^2.
%C A077767 Related to Legendre's conjecture that there is always a prime between 
               two consecutive squares.
%H A077767 T. D. Noe, <a href="b077767.txt">Table of n, a(n) for n=1..1000</a>
%e A077767 a(8)=3 because primes 67, 71 and 79 are between squares 64 and 81
%t A077767 maxN=100; a=Table[0, {maxN}]; maxP=PrimePi[(maxN+1)^2]; For[i=1, i<=maxP, 
               i++, p=Prime[i]; If[Mod[p, 4]==3, j=Floor[Sqrt[p]]; a[[j]]++ ]]; 
               a
%Y A077767 Cf. A002145, A014085, A077766.
%Y A077767 Sequence in context: A060135 A057112 A071956 this_sequence A137163 A072625 
               A090329
%Y A077767 Adjacent sequences: A077764 A077765 A077766 this_sequence A077768 A077769 
               A077770
%K A077767 nonn
%O A077767 1,4
%A A077767 T. D. Noe (noe(AT)sspectra.com), Nov 20 2002

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