A267711 -id:A267711 - cp's OEIS frontend

A380485 Numbers congruent to {0, 1, 2, 3, 4, 5} mod 30.

0, 1, 2, 3, 4, 5, 30, 31, 32, 33, 34, 35, 60, 61, 62, 63, 64, 65, 90, 91, 92, 93, 94, 95, 120, 121, 122, 123, 124, 125, 150, 151, 152, 153, 154, 155, 180, 181, 182, 183, 184, 185, 210, 211, 212, 213, 214, 215, 240, 241, 242, 243, 244, 245, 270, 271, 272, 273, 274, 275, 300, 301, 302, 303, 304, 305, 330, 331, 332, 333

Offset: 1

Antti Karttunen, Feb 03 2025

Numbers k for which A276086(k) is not a multiple of 5.

Odd bisection gives numbers that are congruent to {0, 2, 4} mod 30, thus when halved, congruent to {0, 1, 2} mod 15, thus terms of A267711, numbers k such that k mod 3 = k mod 5.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Cf. A276086, A380484 (characteristic function), A380486 (complement).

Cf. also A267711 (odd bisection halved).

Select[Range[0, 333], Mod[#, 30] < 6 &] (* Amiram Eldar, Feb 03 2025 *)

PARI
```
is_A380485(n) = !((n\6)%5);
```
PARI
```
is_A380485(n) = ((n%30)<6);
```

a(2*n-1) = 2*A267711(n).

A267747 Numbers k such that k mod 2 = k mod 3 = k mod 5.

Original entry on oeis.org

0, 1, 30, 31, 60, 61, 90, 91, 120, 121, 150, 151, 180, 181, 210, 211, 240, 241, 270, 271, 300, 301, 330, 331, 360, 361, 390, 391, 420, 421, 450, 451, 480, 481, 510, 511, 540, 541, 570, 571, 600, 601, 630, 631, 660, 661, 690, 691, 720, 721, 750, 751, 780, 781, 810, 811, 840

Offset: 1

Mikk Heidemaa, Jan 20 2016

Numbers k such that k == 0 or 1 (mod 30). - Robert Israel, Jan 20 2016

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A267711.

[15*n-7*(-1)^n-22: n in [1..60]]; // Vincenzo Librandi, Jan 21 2016

Table[15*n - 7*(-1)^n - 22, {n, 1000}] (* Or *)
Select[ Range[0, 20000], (Mod[#, 2]==Mod[#, 3]==Mod[#, 5]) &]
LinearRecurrence[{1,1,-1},{0,1,30},60] (* Harvey P. Dale, Nov 15 2021 *)

concat(0, Vec(x^2*(29*x+1)/((x-1)^2*(x+1)) + O(x^60))) \\ Colin Barker, Jan 21 2016

a(n) = 15*n - 7*(-1)^n - 22.

G.f.: x^2*(29*x+1)/((x-1)^2*(x+1)).

cp's OEIS Frontend

A380485 Numbers congruent to {0, 1, 2, 3, 4, 5} mod 30.

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A267747 Numbers k such that k mod 2 = k mod 3 = k mod 5.

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