id:A077766 - OEIS Search Results

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Number of primes of form 4k+1 between n^2 and (n+1)^2.

+0
6

0, 1, 1, 1, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 3, 4, 3, 3, 3, 4, 3, 2, 3, 5, 4, 3, 5, 4, 4, 4, 5, 4, 6, 5, 5, 4, 5, 4, 3, 7, 7, 3, 7, 5, 6, 5, 8, 8, 5, 4, 8, 9, 6, 5, 7, 7, 6, 8, 7, 8, 7, 6, 8, 7, 9, 8, 7, 7, 8, 9, 5, 10, 8, 7, 11, 9, 6, 10, 12, 8, 10, 10, 7, 8, 10, 12, 10, 11, 11, 9, 10, 10, 11, 10, 11, 11 (list; graph; listen)

	OFFSET	`1,6`
	COMMENT	`Related to Legendre's conjecture that there is always a prime between two consecutive squares.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..1000`
	EXAMPLE	`a(8)=1 because the prime 73 is between squares 64 and 81.`
	MATHEMATICA	`maxN=100; a=Table[0, {maxN}]; maxP=PrimePi[(maxN+1)^2]; For[i=1, i<=maxP, i++, p=Prime[i]; If[Mod[p, 4]==1, j=Floor[Sqrt[p]]; a[[j]]++ ]]; a`
	CROSSREFS	`Cf. A002144, A014085, A077767.` `Sequence in context: A156748 A075445 A023572 this_sequence A002345 A071694 A072781` `Adjacent sequences: A077763 A077764 A077765 this_sequence A077767 A077768 A077769`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Nov 20 2002`

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Last modified December 17 23:40 EST 2009. Contains 171025 sequences.

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