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A067870 Numbers k such that k and 3^k end with the same digit. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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)

EXAMPLE

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

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

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Last modified September 29 22:48 EDT 2022. Contains 357092 sequences. (Running on oeis4.)