A345019 Numbers whose last digit is refactorable.

1, 2, 8, 9, 11, 12, 18, 19, 21, 22, 28, 29, 31, 32, 38, 39, 41, 42, 48, 49, 51, 52, 58, 59, 61, 62, 68, 69, 71, 72, 78, 79, 81, 82, 88, 89, 91, 92, 98, 99, 101, 102, 108, 109, 111, 112, 118, 119, 121, 122, 128, 129, 131, 132, 138, 139, 141, 142, 148, 149, 151, 152, 158, 159

Offset: 1

Author

Wesley Ivan Hurt, Jun 05 2021

Keywords

• nonn
• easy
• base

Comments

Numbers ending in 1, 2, 8 or 9.

Examples

			158 is in the sequence since 8 is a refactorable number.
		

Links

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

Crossrefs

Cf. A033950 (refactorable numbers).

Programs

Mathematica

Table[10*Floor[(n - 1)/4] + (10 + (-1)^n + 7*Cos[n*Pi/2] - 7*Sin[n*Pi/2]) / 2, {n, 100}]

Formula

a(n) = 10*floor((n-1)/4)+(10+(-1)^n+7*cos(n*Pi/2)-7*sin(n*Pi/2))/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((1+1/sqrt(5))/2)*Pi/5. - Amiram Eldar, Apr 15 2023

G.f.: x*( 1+x+6*x^2+x^3+x^4 ) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Mar 25 2024

a(n) = a(n-1) + a(n-4) - a(n-5). - Wesley Ivan Hurt, Apr 24 2024