A096891 -id:A096891 - cp's OEIS frontend

A096898 Least area/6 of primitive Pythagorean triangles with even leg 4n.

1, 10, 5, 84, 35, 14, 105, 680, 231, 30, 429, 220, 715, 154, 55, 5456, 1615, 390, 2261, 260, 91, 770, 4025, 1976, 5175, 1326, 6525, 140, 8091, 1190, 9889, 43680, 935, 3094, 595, 204, 16835, 4370, 1729, 3080, 22919, 1330, 26445, 836, 285, 7866, 34545, 16240

Offset: 1

Ray Chandler, Jul 14 2004

nonn

Cf. A088557, A088558, A096891-A096900.

A096899 Least inradius of primitive Pythagorean triangles with even leg 4n.

Original entry on oeis.org

1, 3, 2, 7, 6, 3, 10, 15, 14, 4, 18, 15, 22, 12, 5, 31, 30, 20, 34, 15, 6, 28, 42, 39, 46, 36, 50, 7, 54, 35, 58, 63, 30, 52, 21, 8, 70, 60, 42, 55, 78, 35, 82, 24, 9, 76, 90, 87, 94, 84, 66, 40, 102, 92, 10, 63, 78, 100, 114, 56, 118, 108, 45, 127, 30, 11, 130, 72, 102, 91

Offset: 1

Ray Chandler, Jul 14 2004

nonn

Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32. Solution published in Vol. 16, Issue 2, November 2008, p. 32.

Cf. A088557, A088558, A096891-A096900.

A155186 Primes in A155171.

Original entry on oeis.org

2, 7, 29, 101, 107, 197, 227, 457, 647, 829, 1549, 1627, 2221, 2309, 2347, 2521, 2677, 2801, 3181, 3299, 3529, 3541, 3557, 3739, 3769, 4231, 4549, 4871, 4987, 5651, 5827, 5881, 6037, 6079, 6637, 6827, 7517, 7639, 7937, 9787, 11621, 12041, 12329, 13009

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

Numbers p (prime numbers only) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[p],AppendTo[lst,p]]],{n,8!}];lst

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

Original entry on oeis.org

2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

p=1, q=2(prime), a=3, b=4, c=5, s=12-+1 primes, ...

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst

cp's OEIS Frontend

A096898 Least area/6 of primitive Pythagorean triangles with even leg 4n.

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A096899 Least inradius of primitive Pythagorean triangles with even leg 4n.

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A155186 Primes in A155171.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

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cp's OEIS Frontend

A096898 Least area/6 of primitive Pythagorean triangles with even leg 4n.

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Author

Keywords

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A096899 Least inradius of primitive Pythagorean triangles with even leg 4n.

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Author

Keywords

References

Crossrefs

A155186 Primes in A155171.

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Programs

Mathematica

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.

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Programs

Mathematica

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.