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

Author

M. F. Hasler, Jan 22 2014

Keywords

• sign
• base

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.

Examples

			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.
		

Links

• 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

Crossrefs

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

Programs

PARI

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