A161874 -id:A161874 - cp's OEIS frontend

A362026 Smallest unhappy number in base A161874(n).

3, 7, 3, 5, 20, 3, 12, 3, 3, 14, 3, 3, 3, 3, 3, 3, 23, 3, 23, 3, 261, 6, 12

Offset: 1

Lucas A. Brown, Apr 26 2023

This sequence is the list of least unhappy numbers (A161872) with all terms < 3 removed.

			The first term in this sequence corresponds to base 16.  In base 16, 2 is happy because the sequence it generates is 2 -> 4 -> (1,0) -> 1, while 3 is unhappy because the sequence it generates is 3 -> 9 -> (5,1) -> (1,10) -> (6,5) -> (3,13) -> (11,2) -> (7,13) -> (13,10) -> (1,0,13) -> (10,10) -> (12,8) -> (13,0) -> (10,9) -> (11,5) -> (9,2) -> (5,5) -> (3,2) -> (0,13) -> (10,9) -> ..., which repeats with period 6.

Lucas A. Brown, C program.

Cf. A031177, A161872, A161874.

a(n) = A161872(A161874(n)).

A348143 Areas of integer-sided cyclic quadrilaterals whose area equals their perimeter.

Original entry on oeis.org

16, 18, 20, 30

Offset: 1

Frank M Jackson, Oct 02 2021

There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (1, 17/2, 17/2, 16) which has perimeter and area 34.

			The areas or perimeters 16, 18, 20, 30 pertain respectively to cyclic quadrilaterals with sides (4, 4, 4, 4), (3, 3, 6, 6), (2, 5, 5, 8), (5, 5, 6, 14).

Ralph H. Buchholz and James A. MacDougall, Cyclic Polygons with Rational Sides and Area, 2001. JNT 128 (2008) 17-48

Cf. A098030, A290451. First four terms of A161874.

lst={}; Do[s=(a+b+c+d)/2; If[s>a, (K=Sqrt[(s-a)(s-b)(s-c)(s-d)]; If[IntegerQ[K]&&K==2s, AppendTo[lst, Sort@{a,b,c,d}]])], {a, 1, 15}, {b, 1, a}, {c, 1, b}, {d, 1, c}]; lst

cp's OEIS Frontend

A362026 Smallest unhappy number in base A161874(n).

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