Search: id:A100672
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%I A100672
%S A100672 1,1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,0,
%T A100672 1,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,
%U A100672 0,1,1,0,1,1,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1
%N A100672 Second least-significant bit in the binary expansion of the k-th prime.
%C A100672 a(n)=1 iff Prime[n] is a member of A045326 (equivalently, iff Prime[n]-3 
               is divisible by 4)
%H A100672 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Fermats4nPlus1Theorem.html">Fermat's 4n Plus 1 Theorem</a>.
%H A100672 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GaussianPrime.html">Gaussian Prime</a>.
%F A100672 a(n) := Mod[Prime[n], 4] != 2
%e A100672 a(2)=1 because Prime[2]=11_2 (in binary; decimal = 3_10) and its 2^1 
               bit is 1.
%e A100672 a(3)=0 because Prime[3]=101_2 (in binary; decimal = 5_10) and its 2^1 
               bit is 0.
%t A100672 Table[Reverse[RealDigits[Prime[k], 2][[1]]][[2]], {k, 1, 128}]
%Y A100672 Cf. A045326.
%Y A100672 Cf. A002144, A002145.
%Y A100672 equal to 1 minus A098033 [From Steven G. Johnson (stevenj(AT)math.mit.edu), 
               Sep 18 2008]
%Y A100672 Sequence in context: A123594 A145006 A080813 this_sequence A079559 A014577 
               A157926
%Y A100672 Adjacent sequences: A100669 A100670 A100671 this_sequence A100673 A100674 
               A100675
%K A100672 base,nonn
%O A100672 1,1
%A A100672 Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 06 2004

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