A299174 - OEIS

%I #58 Oct 26 2023 09:43:12

%S 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,

%T 50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,

%U 96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144

%N The even positive integers.

%C Possible periods of Post's {00, 1101} tag system. - _Charles R Greathouse IV_, Dec 13 2021

%C Numbers m such that 2^m - m is divisible by 2. - _Bernard Schott_, Dec 15 2021

%H Joss Langford, <a href="https://www.archinterface.co.uk/2018/02/integer-sequences">Simple Integer Sequences</a>

%H James B. Shearer, <a href="http://bit-player.org/wp-content/extras/bph-publications/AmSci-1996-01-Hayes-sequences.pdf">Periods of strings</a>, American Scientist Vol. 84, No. 3 (May-June 1996), p. 207. (See final page of pdf, and see also pp. 3-4 for an introduction.)

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*n, n >= 1.

%F G.f.: 2*x/(1 - x)^2; corrected by _Ilya Gutkovskiy_, Mar 29 2018

%p A299174 := n->2*n;

%t Range[2, 180, 2]

%o (R) seq(2, 180, 2)

%o (PARI) a(n)=2*n \\ _Charles R Greathouse IV_, Dec 13 2021

%Y Equals A005843 without the leading zero.

%Y Bisection of A000027. Complement of A004273. - _Omar E. Pol_, Feb 25 2018

%Y First row of A083140.

%Y Cf. A005408.

%Y Cf. A000325, A047257, A349767.

%Y Essentially the same as A163300, A103517, A051755, A005843 and A004277.

%Y Numbers k that can be written as the sum of j divisors of k (not necessarily distinct) for j=1..10: A000027 (j=1), this sequence (j=2), A355200 (j=3), A354591 (j=4), A355641 (j=5), A356609 (j=6), A356635 (j=7), A356657 (j=8), A356659 (j=9), A356660 (j=10).

%K nonn,easy

%O 1,1

%A _Joss Langford_, Feb 04 2018