A072420 Minimum number of steps needed to transform n into 153 where each step is either tripling or taking the sum of cubes of digits.

4, 4, 3, 5, 4, 3, 5, 4, 3, 4, 5, 4, 4, 4, 3, 7, 2, 2, 4, 4, 4, 6, 4, 3, 6, 5, 2, 7, 5, 3, 5, 4, 5, 5, 3, 3, 5, 5, 3, 5, 5, 3, 6, 5, 2, 6, 5, 6, 6, 4, 1, 6, 6, 5, 6, 5, 3, 6, 3, 3, 7, 5, 5, 6, 6, 5, 4, 4, 3, 5, 5, 2, 6, 5, 5, 4, 5, 4, 5, 4, 2, 6, 4, 6, 6, 5, 6

Offset: 1

Author

Michael Joseph Halm, Jul 31 2002

Keywords

• nonn
• base

Comments

This sequence lists the "toscodicity" of the integers, the minimum number of steps needed to transform the integer into 153 (which happens to be the sum of the cube of its digits, the sum of the first 17 integers and fishily "happens" to be the number of fish mentioned in John 21:10) by the TOSCOD (triple or sum cubes of digits) operator.

The TOSCOD operator is similar to the HOTPO (halve or triple-plus-one) operator used to generate the Collatz sequence. The 51st term is one of the rare "ones". There is only one more at the 135th term before reaching the "zero" point at the 153rd term.

Examples

			f(1) = 4 because tripled 1 yields 3, which cubed yields 27, whose digits cubed yield 8 + 343 = 351, whose digits cubed yield 27 + 125 + 1 = 153, in four steps.
		

References

• M. J. Halm, TOSCOD, Mpossibilities 67, p. 2 (Sept. 1998)

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000
• M. J. Halm, Joycesquean neologisms
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A006577.

Formula

By applying the proper combination of the two alternative operations one minimum number of operations can be determined.

Extensions

a(31) onward corrected by Sean A. Irvine, Sep 29 2024