A186042 Numbers of the form 2*k + 1, 3*k + 2, or 5*k + 3.

1, 2, 3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 18, 19, 20, 21, 23, 25, 26, 27, 28, 29, 31, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 77, 78, 79, 80, 81, 83, 85, 86, 87, 88, 89, 91, 92, 93, 95, 97

Offset: 1

Author

Klaus Brockhaus, Feb 11 2011, Mar 09 2011

Keywords

• nonn
• easy

Comments

n is in the sequence iff n is in A005408 or in A016789 or in A016885.

First differences are periodic with period length 22. Least common multiple of 2, 3, 5 is 30; number of terms <= 30 is 22.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

Crossrefs

Cf. A005408, A016789, A016885.

Programs

Magma

IsA186042:=func< n | exists{ k: k in [0..n div 2] | n in [2*k+1, 3*k+2, 5*k+3] } >; [ n: n in [1..100] | IsA186042(n) ];

Mathematica

LinearRecurrence[{2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1},{1,2,3,5,7,8,9,11,13,14,15,17,18,19,20,21,23,25,26,27,28,29},71] (* Ray Chandler, Jul 12 2015 *)

PARI

isok(n) = (n % 2) || ((n % 3)==2) || ((n % 5)==3); \\ Michel Marcus, Jul 26 2017

Formula

a(n) = a(n-22) + 30.

a(n) = a(n-1) + a(n-22) - a(n-23).

G.f.: x*(x^21 + x^19 + x^17 + x^16 + x^15 + x^13 + x^11 + x^10 + x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1) / ((x - 1)^2*(x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)).