

A072420


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.


1



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

1,1


COMMENTS

The TOSCOD operator is similar to the HOTPO (halve or tripleplusone) 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

Table of n, a(n) for n=1..100.
M. J. Halm, neologisms


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 * A258075 A023530 A233581
Adjacent sequences: A072417 A072418 A072419 * A072421 A072422 A072423


KEYWORD

nonn,base


AUTHOR

Michael Joseph Halm, Jul 31 2002


STATUS

approved



