id:A100672 - OEIS Search Results

Search: id:A100672

Displaying 1-1 of 1 results found.

page 1

Second least-significant bit in the binary expansion of the k-th prime.

+0
3

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; listen)

	OFFSET	`1,1`
	COMMENT	`a(n)=1 iff Prime[n] is a member of A045326 (equivalently, iff Prime[n]-3 is divisible by 4)`
	LINKS	`Eric Weisstein's World of Mathematics, Fermat's 4n Plus 1 Theorem.` `Eric Weisstein's World of Mathematics, Gaussian Prime.`
	FORMULA	`a(n) := Mod[Prime[n], 4] != 2`
	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.`
	MATHEMATICA	`Table[Reverse[RealDigits[Prime[k], 2][[1]]][[2]], {k, 1, 128}]`
	CROSSREFS	`Cf. A045326.` `Cf. A002144, A002145.` `equal to 1 minus A098033 [From Steven G. Johnson (stevenj(AT)math.mit.edu), Sep 18 2008]` `Sequence in context: A123594 A145006 A080813 this_sequence A079559 A014577 A157926` `Adjacent sequences: A100669 A100670 A100671 this_sequence A100673 A100674 A100675`
	KEYWORD	`base,nonn`
	AUTHOR	`Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 06 2004`

page 1

Search completed in 0.002 seconds

Last modified November 29 12:46 EST 2009. Contains 167659 sequences.

AT&T Labs Research