Search: id:A077766
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%I A077766
%S A077766 0,1,1,1,1,2,2,1,2,3,1,2,3,1,3,4,3,3,3,4,3,2,3,5,4,3,5,4,4,4,5,4,6,5,5,
%T A077766 4,5,4,3,7,7,3,7,5,6,5,8,8,5,4,8,9,6,5,7,7,6,8,7,8,7,6,8,7,9,8,7,7,8,9,
%U A077766 5,10,8,7,11,9,6,10,12,8,10,10,7,8,10,12,10,11,11,9,10,10,11,10,11,11
%N A077766 Number of primes of form 4k+1 between n^2 and (n+1)^2.
%C A077766 Related to Legendre's conjecture that there is always a prime between 
               two consecutive squares.
%H A077766 T. D. Noe, <a href="b077766.txt">Table of n, a(n) for n=1..1000</a>
%e A077766 a(8)=1 because the prime 73 is between squares 64 and 81.
%t A077766 maxN=100; a=Table[0, {maxN}]; maxP=PrimePi[(maxN+1)^2]; For[i=1, i<=maxP, 
               i++, p=Prime[i]; If[Mod[p, 4]==1, j=Floor[Sqrt[p]]; a[[j]]++ ]]; 
               a
%Y A077766 Cf. A002144, A014085, A077767.
%Y A077766 Sequence in context: A156748 A075445 A023572 this_sequence A002345 A071694 
               A072781
%Y A077766 Adjacent sequences: A077763 A077764 A077765 this_sequence A077767 A077768 
               A077769
%K A077766 nonn
%O A077766 1,6
%A A077766 T. D. Noe (noe(AT)sspectra.com), Nov 20 2002

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