A058529 -id:A058529 - cp's OEIS frontend

A116509 Values of c in a^2 + b^2 = c^2 where b - a = 31 and gcd(a,b)=1.

41, 109, 221, 629, 1285, 3665, 7489, 21361, 43649, 124501, 254405, 725645, 1482781, 4229369, 8642281, 24650569, 50370905, 143674045, 293583149, 837393701, 1711127989, 4880688161, 9973184785, 28446735265, 58127980721

Offset: 1

Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 21 2006

nonn

b - a = 31 is the fifth term of A058529

			c(5)= 6*221-41=1285 and 893^2 + 924^2 = 1285^2 and 924-893=31 and gcd(893,924)=1

RecurrenceTable[{a[1]==41,a[2]==109,a[3]==221,a[4]==629,a[n]==6a[n-2]-a[n-4]},a,{n,30}] (* Harvey P. Dale, Aug 01 2021 *)

c(1)=41,c(2)=109,c(3)=221,c(4)=629,c(n)=6*c(n-2)-c(n-4)

A253408 Values of difference z-y that solve equation x^2 + y^2 = z^2 + 2.

Original entry on oeis.org

-1, 1, 7, 17, 23, 31, 41, 47, 49, 71, 73, 79, 89, 97, 103, 113, 119, 127, 137, 151, 161, 167, 191, 193, 199, 217, 223, 233, 239, 241, 257, 263, 271, 281, 287, 289, 311, 313, 329, 337, 343, 353, 359, 367, 383, 391, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487

Offset: 1

Carmine Suriano, Jan 05 2015

sign

All values are congruent to +-1 (mod 8).

			a(3)=7 because 25^2 + 41^2 = 48^2 + 2 and 48 - 41 = 7.

Cf. A058529.

a(n)^2 mod 8 = 1.

a(n) = A058529(n-1), n>1.

cp's OEIS Frontend

A116509 Values of c in a^2 + b^2 = c^2 where b - a = 31 and gcd(a,b)=1.

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