A236338 Number of iterations of A235600 to reach 1 when starting with n, or -1 if 1 is never reached. (A235600(x) = x/sum_of_digits(x) if this is an integer, otherwise A235600(x) = x.)

0, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1

Offset

1,12

Comments

Based on an idea from N. J. A. Sloane, cf. link.

Numbers n = 10^k and also numbers not divisible by their digital sum A007953, are fixed points of A235600, therefore a(n) = -1 for these, except for a(1) = 0, cf. Example.

A235601(k) is the smallest n for which a(n) = k.

Links

Table of n, a(n) for n=1..68.

N. J. A. Sloane, in reply to D. W. Wilson, Re: As much as I hate "base" sequences..., SeqFan list, Jan 18 2014

David W. Wilson, Ray Chandler, Alonso Del Arte, M. F. Hasler, Hans Havermann, Alex Meiburg, N. J. A. Sloane, Hugo Van Der Sanden, and Allan Wechsler, As much as I hate "base" sequences..., Copies of various posts to the Sequence Fans Mailing List, Circa January 2014. Assembled by N. J. A. Sloane, Dec 23 2024

Example

a(1) = 0 since no iteration of A235600 is needed to reach 1.
a(n) = 1 for 1 <= n <= 9, since these n are equal to (thus divisible by) their sum of digits A007953(n), and 1 is reached upon the first iteration of A235600 (which consists of dividing n by its sum of digits).
a(10) = -1 since A007953(10) = 1 and therefore application of A235600 yields a constant sequence that never reaches 1.
a(11) = -1 since 11 is not divisible by A007953(11) = 2 and therefore application of A235600 yields a constant sequence that never reaches 1.
a(12) = 2 since A235600(12) = 12/(1+2) = 4 and A235600(4) = 4/4 = 1, reached after 2 iterations.

Prog

(PARI) A236338 = n -> for(i=0, 999, n==1&&return(i); if(n%sumdigits(n)||n==n\=sumdigits(n), return(-1)))

Crossrefs

Cf. A005349, A007953, A114440, A235600, A235601.

Sequence in context: A324907 A331295 A325133 * A284259 A250068 A214566

Adjacent sequences: A236335 A236336 A236337 * A236339 A236340 A236341

Keyword

sign,base

Author

M. F. Hasler, Jan 22 2014

Status

approved