id:A130911 - OEIS Search Results

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Prime race between evil primes (A027699) and odious primes (A027697).

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1, 0, -1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 5, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 8, 9, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 21, 20, 19, 20, 19, 18, 19, 18, 19, 18, 19, 18, 19, 18, 17, 16, 15, 14, 15, 14, 15, 14, 13, 14, 13, 14, 15, 16, 17, 18, 19, 20, 19, 20, 19, 20, 19, 18, 19, 20, 21, 20, 19 (list; graph; listen)

	OFFSET	`1,6`
	COMMENT	`Shevelev conjectures that a(n)>=0 for n>3. Surprisingly, the conjecture also appears to be true if we count zeros instead of ones in the binary representation of prime numbers.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..10000` `Vladimir Shevelev, A conjecture on primes and a step towards justification`
	FORMULA	`a(n) = (number of odious primes <= prime(n)) - (number of evil primes <= prime(n))`
	MATHEMATICA	`cnt=0; Table[p=Prime[n]; If[EvenQ[Count[IntegerDigits[p, 2], 1]], cnt--, cnt++ ]; cnt, {n, 10000}]`
	CROSSREFS	`Cf. A095005, A095006.` `Sequence in context: A137178 A101666 A035224 this_sequence A118829 A118832 A122807` `Adjacent sequences: A130908 A130909 A130910 this_sequence A130912 A130913 A130914`
	KEYWORD	`nice,sign`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jun 08 2007`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

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