A077766 Number of primes of form 4k+1 between n^2 and (n+1)^2.

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

Offset: 1

Author

T. D. Noe, Nov 20 2002

Keywords

• nonn

Comments

Related to Legendre's conjecture that there is always a prime between two consecutive squares.

Examples

			a(8)=1 because the prime 73 is between squares 64 and 81.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A002144, A014085, A077767.

Programs

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