A262389 Numbers whose last digit is composite.

4, 6, 8, 9, 14, 16, 18, 19, 24, 26, 28, 29, 34, 36, 38, 39, 44, 46, 48, 49, 54, 56, 58, 59, 64, 66, 68, 69, 74, 76, 78, 79, 84, 86, 88, 89, 94, 96, 98, 99, 104, 106, 108, 109, 114, 116, 118, 119, 124, 126, 128, 129, 134, 136, 138, 139, 144, 146, 148, 149

Offset

1,1

Comments

Numbers ending in 4, 6, 8 or 9.

Union of A017317, A017341, A017365 and A017377.

Subsequence of A118951 (numbers containing at least one composite digit).

Complement of (A197652 Union A260181).

Links

Table of n, a(n) for n=1..60.

Gerald Hillier and Didier Lachieze, Last Digit Composite.

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

Formula

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4)/2)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(10-2*sqrt(5))*Pi - sqrt(5)*arccoth(3/sqrt(5)) - 4*log(2))/20. - Amiram Eldar, Jul 30 2024

Maple

A262389:=n->(5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4)/2)/2: seq(A262389(n), n=1..100);

Mathematica

Table[(5n+1-(-1)^n+(3+(-1)^n)*(-1)^((2n-3-(-1)^n)/4)/2)/2, {n, 100}]
LinearRecurrence[{1, 0, 0, 1, -1}, {4, 6, 8, 9, 14}, 80] (* Vincenzo Librandi, Sep 21 2015 *)
CoefficientList[Series[(4 + 2*x + 2*x^2 + x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 80}], x] (* Wesley Ivan Hurt, Sep 21 2015 *)
Select[Range[200], CompositeQ[Mod[#, 10]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 21 2019 *)

Prog

(Magma) [(5*n+1-(-1)^n+(3+(-1)^n)*(-1)^((2*n-3-(-1)^n) div 4) div 2) div 2: n in [1..70]]; // Vincenzo Librandi, Sep 21 2015

Crossrefs

Cf. A017317, A017341, A017365, A017377.

Cf. A118951, A197652, A260181 (last digit is prime).

Sequence in context: A119492 A285586 A118951 * A254755 A275624 A228019

Adjacent sequences: A262386 A262387 A262388 * A262390 A262391 A262392

Keyword

nonn,base,easy

Author

Wesley Ivan Hurt, Sep 21 2015

Extensions

Name edited by Jon E. Schoenfield, Feb 15 2018

Status

approved