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A100672 Second least-significant bit in the binary expansion of the n-th prime. 6
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n)=1 iff prime(n) is a member of A045326 (equivalently for n>1, iff prime(n)-3 is divisible by 4).

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Fermat's 4n Plus 1 Theorem.

Eric Weisstein's World of Mathematics, Gaussian Prime.

FORMULA

a(n) = 1-A098033(n), n>1. Steven G. Johnson (stevenj(AT)math.mit.edu), Sep 18 2008

a(n) = ((ithprime(n)-2) mod 4) mod 3 (Conjectured). [From Gary Detlefs, Dec 06 2011]

EXAMPLE

a(2)=1 because Prime[2]=11_2 (in binary; decimal = 3_10) and its 2^1 bit is 1.

a(3)=0 because Prime[3]=101_2 (in binary; decimal = 5_10) and its 2^1 bit is 0.

MAPLE

A100672 := proc(n)

        if n = 1 then

                1 ;

        else

                ((ithprime(n) mod 4)-1)/2;

        end if;

end proc: # R. J. Mathar, Oct 06 2011

seq(((ithprime(n)-2) mod 4) mod 3, n= 1 ..300); [Gary Detlefs, Dec 06 2011]

MATHEMATICA

Table[Reverse[RealDigits[Prime[k], 2][[1]]][[2]], {k, 1, 128}]

PROG

(PARI) for(k=1, 105, print1( bittest(prime(k), 1), ", ")) - W. Bomfim, Jan 18, 2011

CROSSREFS

Cf. A045326, A002144, A002145.

Sequence in context: A123594 A145006 A080813 * A079559 A175480 A229062

Adjacent sequences:  A100669 A100670 A100671 * A100673 A100674 A100675

KEYWORD

base,nonn,easy

AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 06 2004

STATUS

approved

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Last modified April 19 11:07 EDT 2014. Contains 240749 sequences.