A067749 Numbers k such that k and 3^k end with the same two digits.

87, 187, 287, 387, 487, 587, 687, 787, 887, 987, 1087, 1187, 1287, 1387, 1487, 1587, 1687, 1787, 1887, 1987, 2087, 2187, 2287, 2387, 2487, 2587, 2687, 2787, 2887, 2987, 3087, 3187, 3287, 3387, 3487, 3587, 3687, 3787, 3887, 3987, 4087, 4187, 4287, 4387, 4487, 4587, 4687

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

a(n) = 100*n - 13.

From Elmo R. Oliveira, Jun 09 2025: (Start)

G.f.: x*(13*x + 87)/(1 - x)^2.

E.g.f.: 13 + exp(x)*(100*x - 13).

a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)

Mathematica

100*Range[50]-13 (* or *) LinearRecurrence[{2, -1}, {87, 187}, 50] (* Harvey P. Dale, Jul 18 2016 *)

Prog

(PARI) a(n) = 100*n - 13; \\ Jinyuan Wang, Apr 05 2020
(PARI) my(x='x+O('x^48)); Vec(x*(87+13*x)/(-1+x)^2) \\ Elmo R. Oliveira, Jun 09 2025
(Magma) [100*n - 13 : n in [1..100]]; // Wesley Ivan Hurt, Feb 13 2026

Crossrefs

Sequence in context: A324111 A044419 A044800 * A063349 A101259 A063336

Adjacent sequences: A067746 A067747 A067748 * A067750 A067751 A067752

Keyword

nonn,base,easy

Author

Benoit Cloitre, Mar 07 2002

Extensions

More terms from Elmo R. Oliveira, Jun 09 2025

Status

approved