A375241 Nontriangular numbers with digital root in {1, 3, 6, 9}.

9, 12, 18, 19, 24, 27, 30, 33, 37, 39, 42, 46, 48, 51, 54, 57, 60, 63, 64, 69, 72, 73, 75, 81, 82, 84, 87, 90, 93, 96, 99, 100, 102, 108, 109, 111, 114, 117, 118, 123, 126, 127, 129, 132, 135, 138, 141, 144, 145, 147, 150, 154, 156, 159, 162, 163, 165, 168, 172

Offset: 1

Author

Stefano Spezia, Aug 07 2024

Keywords

• nonn
• base
• easy

Comments

Except for 0, the triangular numbers (A000217) have digital root in {1, 3, 6, 9} (A055264), but the reverse is not always true since there are nontriangular numbers (A014132) with digital root in the same set.

References

• Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See p. 190.

Links

• Stefano Spezia, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A014132 and A055264. Complement of A375242 in A014132.

Cf. A000217, A010888.

Programs

Mathematica

A010888[n_]:=If[n>0,n - 9*Floor[(n-1)/9],0]; Select[Range[0,200], !OddQ[Sqrt[1+8#]] && MemberQ[{1,3,6,9},A010888[#]] &]