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 A077766 Number of primes of form 4k+1 between n^2 and (n+1)^2. 8
 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 Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe) 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: A333252 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 May 21 08:44 EDT 2022. Contains 353908 sequences. (Running on oeis4.)