id:A069160 - OEIS Search Results

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Number of primes p such that n^2 < p < n^2 + pi(n), where pi(n) is the number of primes less than n.

+0
1

0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 3, 1, 2, 3, 1, 3, 2, 3, 1, 0, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 4, 2, 1, 2, 2, 3, 0, 2, 3, 3, 2, 2, 0, 2, 2, 2, 2, 3, 2, 3, 1, 3, 2, 1, 5, 2, 3, 2, 4, 2, 5, 3, 3, 4, 4, 1, 2, 3, 3, 3, 5, 3, 3 (list; graph; listen)

	OFFSET	`1,10`
	COMMENT	`A more restrictive version of the conjecture that there is always a prime between n^2 and (n+1)^2.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..10000`
	EXAMPLE	`a(10)= 2 because pi(10) = 4 and there are 2 primes between 100 and 104.`
	MATHEMATICA	`maxN=100; lst={}; For[i=1, i<maxN, i++, n=i^2; cnt=0; k=1; While[k<PrimePi[i], If[PrimeQ[n+k], cnt++ ]; k++ ]; AppendTo[lst, cnt]]; lst`
	CROSSREFS	`Cf. A000720, A014085.` `Sequence in context: A144874 A039971 A112020 this_sequence A089616 A089615 A089731` `Adjacent sequences: A069157 A069158 A069159 this_sequence A069161 A069162 A069163`
	KEYWORD	`easy,nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Apr 09 2002`

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Last modified December 13 23:45 EST 2009. Contains 170824 sequences.

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