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

Author

Eric Angelini and Giorgos Kalogeropoulos, Mar 09 2024

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A370408.

Programs

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]