This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081615 #47 Jul 22 2020 05:23:59
%S A081615 1,2,3,14,21,47,158,237,533,1199,4046,6069,13655,46085,103691,1181102,
%T A081615 1771653,3986219,102162425,229865456,344798184,517197276,775795914,
%U A081615 1163693871,3927466814,5891200221,13255200497,29824201118,44736301677,100656678773,226477527239,764361654431,2579720583704,3869580875556,5804371313334,8706556970001,19589753182502,29384629773753,66115416990944,99173125486416
%N A081615 Subsequence of A005428 where state = 2.
%C A081615 Excluding the initial 1, the values of n such that A054995(n) = 2. - _Ryan Brooks_, Jul 17 2020
%C A081615 From _Petros Hadjicostas_, Jul 20 2020: (Start)
%C A081615 From a(1) = 2 to a(22) = 775795914, the values appear in Table 18 (p. 374) in Schuh (1968) under the Survivor No. 2 column (in a variation of Josephus's counting off game where m people on a circle are labeled 1 through m and every third person drops out).
%C A081615 a(23) here is 1163693871 but 1063693871 in Schuh (1968). Burde (1987) agrees with Schuh (1968). See the table on p. 207 of the paper (with q = 1).
%C A081615 It seems Schuh (1968) made a calculation error and Burde (1987) copied it. See my comment for A073941 for more details. (End)
%D A081615 Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968. [See Table 18, p. 374.]
%H A081615 David A. Corneth, <a href="/A081615/b081615.txt">Table of n, a(n) for n = 0..2862</a>
%H A081615 K. Burde, <a href="http://dx.doi.org/10.1016/0022-314X(87)90078-3">Das Problem der Abzählreime und Zahlentwicklungen mit gebrochenen Basen [The problem of counting rhymes and number expansions with fractional bases]</a>, J. Number Theory 26(2) (1987), 192-209. [The author deals with the representation of n in fractional bases k/(k-1) and its relation to counting-off games. Here k = 3. See the table on p. 207. See also the review in MathSciNet (MR0889384) by R. G. Stoneham.]
%H A081615 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%o A081615 (PARI) /* In the program below, we use a truncated version of either A005428 or A073941 and choose those terms that correspond to "state" or "number of last survivor" equal to 2. See A073941 or Schuh (1968) for more details. */
%o A081615 first(n) = {my(res = vector(n), t = 1, wn = wo = gn = go = 2); res[1] = 1; for(i = 1, oo, c = wo % 2; if(go == 2, t++; res[t] = wo; if(t >= n, return(res))); wn = floor(wo*3/2) + c * (2 - go); gn = 3 * c + go * (-1)^c; wo = wn; go = gn; )} \\ _David A. Corneth_ and _Petros Hadjicostas_, Jul 21 2020
%Y A081615 Cf. A005428, A073941, A081614.
%K A081615 nonn,easy
%O A081615 0,2
%A A081615 _N. J. A. Sloane_, Apr 23 2003
%E A081615 More terms from _Hans Havermann_, Apr 23 2003