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

1,1

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

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[#]] &]

Crossrefs

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

Cf. A000217, A010888.

Sequence in context: A356842 A174525 A141552 * A317720 A162822 A087269

Adjacent sequences: A375238 A375239 A375240 * A375242 A375243 A375244

Keyword

nonn,base,easy

Author

Stefano Spezia, Aug 07 2024

Status

approved