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A077766 Number of primes of form 4k+1 between n^2 and (n+1)^2. 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; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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: A236573 A293375 A232174 * A273110 A284155 A002345

Adjacent sequences:  A077763 A077764 A077765 * A077767 A077768 A077769

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 20 2002

STATUS

approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)