%I #39 Jul 16 2024 17:03:27
%S 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,
%T 0,1,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,
%U 1,0,0,1,1,0,1,1,0,0,0,0,1,0,1,0,1,1,0,0,0,1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1
%N Second least-significant bit in the binary expansion of the n-th prime.
%C a(n)=1 iff prime(n) is a member of A045326 (equivalently for n>1, iff prime(n)-3 is divisible by 4).
%H Amiram Eldar, <a href="/A100672/b100672.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fermats4nPlus1Theorem.html">Fermat's 4n Plus 1 Theorem</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>.
%F a(n) = 1-A098033(n), n>1. - Steven G. Johnson (stevenj(AT)math.mit.edu), Sep 18 2008
%F a(n) = floor(prime(n)/2) mod 2. - _Alois P. Heinz_, Jul 16 2024
%e a(2)=1 because prime(2)=11_2 (in binary; decimal = 3_10) and its 2^1 bit is 1.
%e a(3)=0 because prime(3)=101_2 (in binary; decimal = 5_10) and its 2^1 bit is 0.
%p A100672 := proc(n)
%p if n = 1 then
%p 1 ;
%p else
%p ((ithprime(n) mod 4)-1)/2;
%p end if;
%p end proc: # _R. J. Mathar_, Oct 06 2011
%t Table[Reverse[RealDigits[Prime[k], 2][[1]]][[2]], {k, 1, 128}]
%o (PARI) for(k=1,105,print1( bittest(prime(k), 1), ", ")) \\ _Washington Bomfim_, Jan 18 2011
%o (Python)
%o from sympy import prime
%o def A100672(n): return int(prime(n)>>1&1) # _Chai Wah Wu_, Jun 23 2023
%Y Cf. A000040, A045326, A002144, A002145.
%K base,nonn,easy
%O 1,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 06 2004