A375852 Numbers congruent to {0, 1, 3, 6, 7, 9, 12, 15} mod 18.

0, 1, 3, 6, 7, 9, 12, 15, 18, 19, 21, 24, 25, 27, 30, 33, 36, 37, 39, 42, 43, 45, 48, 51, 54, 55, 57, 60, 61, 63, 66, 69, 72, 73, 75, 78, 79, 81, 84, 87, 90, 91, 93, 96, 97, 99, 102, 105, 108, 109, 111, 114, 115, 117, 120, 123, 126, 127, 129, 132, 133, 135, 138, 141, 144, 145, 147, 150

Offset: 1

Author

Jules Beauchamp, Aug 31 2024

Keywords

• nonn
• easy

Comments

Appears to be the union of A061641 (pure numbers in the Collatz (3x+1) iteration, also called pure hailstone numbers) and A309180 (unsuspected numbers to check in the Collatz conjecture).

The differences are periodic: 1, 2, 3, 1, 2, 3, 3, 3.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-1).

Crossrefs

Cf. A061641, A309180.

Programs

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 3, 6, 7, 9, 12, 15}, Mod[#, 18]] &] (* Amiram Eldar, Aug 31 2024 *)

Formula

From Stefano Spezia, Sep 03 2024: (Start)

G.f.: x^2*(1 + x + 2*x^2 - x^3 + 3*x^4 + 3*x^6)/((1 - x)^2*(1 + x^2 + x^4 + x^6)).

E.g.f.: ((9*x - 14)*cosh(x) + sin(x) + 2*sqrt(2)*cosh(x/sqrt(2))*sin(x/sqrt(2)) + (9*x - 14)*sinh(x) + 2*(6 + cos(x) + (sqrt(2)*cos(x/sqrt(2)) + sin(x/sqrt(2)))*sinh(x/sqrt(2))))/4. (End)