A067844 Numbers k such that k and 2^k end with the same digit.

14, 16, 34, 36, 54, 56, 74, 76, 94, 96, 114, 116, 134, 136, 154, 156, 174, 176, 194, 196, 214, 216, 234, 236, 254, 256, 274, 276, 294, 296, 314, 316, 334, 336, 354, 356, 374, 376, 394, 396, 414, 416, 434, 436, 454, 456, 474, 476, 494, 496, 514, 516, 534, 536

Offset

1,1

Comments

Also numbers k such that k and (2^(2*h+1))^k (for n>=0) end with the same digit. - Bruno Berselli, Dec 13 2018

Links

Table of n, a(n) for n=1..54.

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

Formula

From Colin Barker, Dec 01 2012: (Start)

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

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

a(n) = 10*n - 4*(-1)^n. (End)

Example

2^36 = 68719476736 hence 36 is in the sequence.

Mathematica

LinearRecurrence[{1, 1, -1}, {14, 16, 34}, 70] (* Harvey P. Dale, Aug 19 2021 *)

Prog

(PARI) isok(n) = (2^n - n) % 10 == 0; \\ Michel Marcus, Nov 23 2013

Crossrefs

Cf. A064541.

Sequence in context: A175887 A305885 A224402 * A015877 A192290 A152010

Adjacent sequences: A067841 A067842 A067843 * A067845 A067846 A067847

Keyword

nonn,base,easy

Author

Benoit Cloitre, Mar 07 2002

Extensions

Example corrected by Michel Marcus, Nov 23 2013

Status

approved