A063149 Composite numbers which in base 5 contain their largest proper factor as a substring.

25, 35, 55, 65, 85, 95, 115, 125, 145, 155, 175, 185, 205, 215, 235, 245, 265, 275, 295, 305, 325, 335, 355, 365, 385, 395, 415, 425, 445, 455, 475, 485, 505, 515, 535, 545, 565, 575, 595, 605, 625, 635, 655, 665, 685, 695, 715, 725, 745, 755, 775, 785, 805

Offset: 1

Author

Robert G. Wilson v, Aug 08 2001

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A062238.

Programs

Mathematica

Do[ If[ !PrimeQ[ n ] && StringPosition[ ToString[ FromDigits[ IntegerDigits[ n, 5 ] ] ], ToString[ FromDigits[ IntegerDigits[ Divisors[ n ] [ [ -2 ] ], 5 ] ] ] ] != {}, Print[ n ] ], {n, 2, 1000} ]

PARI

a(n)=([0,1,0; 0,0,1; -1,1,1]^(n-1)*[25;35;55])[1,1] \\ Charles R Greathouse IV, Jun 05 2024

Formula

a(n) = 30*n-a(n-1) for n>1, a(1)=25. - Vincenzo Librandi, Aug 07 2010

From Chai Wah Wu, Jun 05 2024: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.

G.f.: x*(-5*x^2 + 10*x + 25)/((x - 1)^2*(x + 1)). (End)