A081615 Subsequence of A005428 where state = 2.

1, 2, 3, 14, 21, 47, 158, 237, 533, 1199, 4046, 6069, 13655, 46085, 103691, 1181102, 1771653, 3986219, 102162425, 229865456, 344798184, 517197276, 775795914, 1163693871, 3927466814, 5891200221, 13255200497, 29824201118, 44736301677, 100656678773, 226477527239, 764361654431, 2579720583704, 3869580875556, 5804371313334, 8706556970001, 19589753182502, 29384629773753, 66115416990944, 99173125486416

Offset

0,2

Comments

Excluding the initial 1, the values of n such that A054995(n) = 2. - Ryan Brooks, Jul 17 2020

From Petros Hadjicostas, Jul 20 2020: (Start)

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).

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).

It seems Schuh (1968) made a calculation error and Burde (1987) copied it. See my comment for A073941 for more details. (End)

References

Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968. [See Table 18, p. 374.]

Links

David A. Corneth, Table of n, a(n) for n = 0..2862

K. Burde, Das Problem der Abzählreime und Zahlentwicklungen mit gebrochenen Basen [The problem of counting rhymes and number expansions with fractional bases], 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.]

Index entries for sequences related to the Josephus Problem

Prog

(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. */
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

Crossrefs

Cf. A005428, A073941, A081614.

Sequence in context: A160218 A208983 A337609 * A157903 A024478 A025090

Adjacent sequences: A081612 A081613 A081614 * A081616 A081617 A081618

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 23 2003

Extensions

More terms from Hans Havermann, Apr 23 2003

Status

approved