A067870 Numbers k such that k and 3^k end with the same digit.

7, 13, 27, 33, 47, 53, 67, 73, 87, 93, 107, 113, 127, 133, 147, 153, 167, 173, 187, 193, 207, 213, 227, 233, 247, 253, 267, 273, 287, 293, 307, 313, 327, 333, 347, 353, 367, 373, 387, 393, 407, 413, 427, 433, 447, 453, 467, 473, 487, 493, 507, 513, 527, 533

Offset

1,1

Comments

Also numbers k such that k^k ends with 3. - Bruno Berselli, Dec 11 2018

Numbers congruent to {7, 13} mod 20. - Amiram Eldar, Feb 27 2023

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(2*n+1) = 20*n-13, a(2*n) = 20*n-7.

a(n) = 20*(n-1)-a(n-1) for n>1, a(1)=7. - Vincenzo Librandi, Aug 08 2010

From Colin Barker, Apr 06 2020: (Start)

G.f.: x*(7 + 6*x + 7*x^2) / ((1 - x)^2*(1 + x)).

a(n) = -5 - 2*(-1)^n + 10*n for n>0.

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

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/20)*Pi/20. - Amiram Eldar, Feb 27 2023

Example

3^13 = 1594323 hence 13 is in the sequence.

Mathematica

LinearRecurrence[{1, 1, -1}, {7, 13, 27}, 50] (* Amiram Eldar, Feb 27 2023 *)

Prog

(PARI) a(n) = (5*(2*n-1)*(-1)^n - 2)*(-1)^n; \\ Jinyuan Wang, Apr 06 2020
(PARI) Vec(x*(7 + 6*x + 7*x^2) / ((1 - x)^2*(1 + x)) + O(x^50)) \\ Colin Barker, Apr 06 2020

Crossrefs

Sequence in context: A205541 A072579 A337433 * A147258 A146718 A146646

Adjacent sequences: A067867 A067868 A067869 * A067871 A067872 A067873

Keyword

nonn,base,easy

Author

Benoit Cloitre, Mar 07 2002

Status

approved