A382097 Sum of the legs of the unique primitive Pythagorean triple whose inradius is the n-th prime and whose short leg is an odd number.

17, 31, 71, 127, 287, 391, 647, 799, 1151, 1799, 2047, 2887, 3527, 3871, 4607, 5831, 7199, 7687, 9247, 10367, 10951, 12799, 14111, 16199, 19207, 20807, 21631, 23327, 24199, 25991, 32767, 34847, 38087, 39199, 44999, 46207, 49927, 53791, 56447, 60551

Offset

1,1

References

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Links

Table of n, a(n) for n=1..40.

Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Formula

a(n) = 2*(prime(n))^2 + 4*prime(n) + 1.

a(n) = A367573(n,1) + A367573(n,2).

Example

For n=2, the short leg is A367573(2,1) = 7 and the long leg is A367573(2,2) = 24 so the sum of the legs is then a(2) = 7 + 24 = 31.

Mathematica

a=Table[Prime[n], {n, 1, 40}]; Apply[Join, Map[{2#^2+4#+1}&, a]]

Crossrefs

Cf. A034953, A367573, A382070, A098996.

Sequence in context: A087166 A167496 A370851 * A164041 A085598 A163443

Adjacent sequences: A382094 A382095 A382096 * A382098 A382099 A382100

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Mar 15 2025

Status

approved