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A345019
Numbers whose last digit is refactorable.
1
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
1,2
COMMENTS
Numbers ending in 1, 2, 8 or 9.
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
EXAMPLE
158 is in the sequence since 8 is a refactorable number.
MATHEMATICA
Table[10*Floor[(n - 1)/4] + (10 + (-1)^n + 7*Cos[n*Pi/2] - 7*Sin[n*Pi/2]) / 2, {n, 100}]
CROSSREFS
Cf. A033950 (refactorable numbers).
Sequence in context: A282636 A019511 A103190 * A116039 A030334 A338807
KEYWORD
nonn,easy,base
AUTHOR
Wesley Ivan Hurt, Jun 05 2021
STATUS
approved