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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.
2
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
1,1
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.
REFERENCES
M. J. Halm, TOSCOD, Mpossibilities 67, p. 2 (Sept. 1998)
LINKS
Sean A. Irvine, Java program (github)
FORMULA
By applying the proper combination of the two alternative operations one minimum number of operations can be determined.
EXAMPLE
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.
CROSSREFS
Cf. A006577.
Sequence in context: A202393 A073321 A055620 * A377049 A258075 A286296
KEYWORD
nonn,base
AUTHOR
Michael Joseph Halm, Jul 31 2002
EXTENSIONS
a(31) onward corrected by Sean A. Irvine, Sep 29 2024
STATUS
approved