A261234 a(n) = number of steps to reach (3^n)-1 when starting from k = (3^(n+1))-1 and repeatedly applying the map that replaces k with k - (sum of digits in base-3 representation of k).

1, 2, 5, 12, 29, 74, 196, 530, 1445, 3956, 10862, 29901, 82592, 229233, 639967, 1797288, 5073707, 14381347, 40890492, 116559600, 333043360, 953890490, 2738788806, 7881915828, 22729464587, 65652788211, 189866467219, 549596773550, 1592118137130, 4615680732717, 13392399641613, 38894563977633, 113074467549440, 329080350818600, 958725278344368, 2795854777347489

Offset

0,2

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 0..100

Antti Karttunen, Naive C-program for computing the terms of A261234, A261236 and A261237 at the same time

Hiroaki Yamanouchi, Fast Python-program for computing terms of A213709, A261234 and analogous sequences in other bases

Formula

a(n) = A261236(n) + A261237(n).

Mathematica

Table[Length@ NestWhileList[# - Total@ IntegerDigits[#, 3] &, 3^(n + 1) - 1, # > 3^n - 1 &] - 1, {n, 0, 16}] (* Michael De Vlieger, Jun 27 2016 *)

Prog

(Scheme, three variants)
(definec (A261234 n) (let ((end (- (A000244 n) 1))) (let loop ((k (- (A000244 (+ 1 n)) 1)) (s 0)) (if (= k end) s (loop (* 2 (A054861 k)) (+ 1 s))))))
(define (A261234 n) (- (A261233 (+ 1 n)) (A261233 n)))
(define (A261234 n) (- (A261231 (A000244 (+ 1 n))) (A261231 (A000244 n))))

Crossrefs

Cf. A000244, A054861, A261231, A261230.

First differences of A261232 and A261233.

Sum of A261236 and A261237.

Cf. A261235 (first differences of this sequence).

Cf. also A213709.

Sequence in context: A036671 A152171 A132807 * A368984 A324787 A333888

Adjacent sequences: A261231 A261232 A261233 * A261235 A261236 A261237

Keyword

nonn,base

Author

Antti Karttunen, Aug 13 2015

Extensions

a(23)-a(35) from Hiroaki Yamanouchi, Aug 16 2015

Status

approved