A371060 Lexicographically earliest sequence of distinct terms such that every triplet of successive digits (seen as side lengths) can form a triangle.

1, 2, 21, 22, 3, 4, 5, 6, 7, 8, 9, 28, 72, 65, 24, 32, 23, 31, 33, 13, 34, 25, 42, 43, 35, 36, 44, 14, 41, 441, 442, 45, 26, 52, 54, 46, 37, 53, 55, 15, 51, 551, 552, 56, 27, 62, 66, 16, 61, 661, 662, 67, 38, 63, 57, 39, 73, 64, 47, 48, 58, 49, 68, 59, 69, 74, 75, 76, 77, 17, 71, 771, 772

Offset

1,2

Comments

In a triangle, the sum of any two side lengths is greater than that of the third, so that x + y > z.

Links

Table of n, a(n) for n=1..73.

Eric Angelini and Giorgos Kalogeropoulos, Triangles with digits, Personal blog, March 2024.

Example

The first triplet of digits (1, 2, 2) forms an isosceles triangle with basis 1 and sides 2 and 2;
the second triplet (2, 2, 1) forms another isosceles triangle with basis 1 and sides 2 and 2;
the fifth triplet (2, 2, 3) forms another isosceles triangle with basis 3 and sides 2 and 2;
the sixth triplet (2, 3, 4) forms a scalene triangle with sides 2, 3 and 4; etc.

Mathematica

g[1]=1; g[2]=2; g[n_]:=g[n]=(k=1; While[MemberQ[ar=Array[g, n-1], k]|| !And@@(({a, b, c}=#; And@@{a+b>c, b+c>a, a+c>b})&/@Partition[Flatten[IntegerDigits/@Join[ar, {k}]], 3, 1]), k++]; k); Array[g, 80]

Crossrefs

Cf. A370408.

Sequence in context: A140268 A106422 A320523 * A171549 A355404 A077678

Adjacent sequences: A371057 A371058 A371059 * A371062 A371063 A371064

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Mar 09 2024

Status

approved