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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.

%I A072420 #17 Sep 29 2024 21:09:29
%S A072420 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,
%T A072420 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,
%U A072420 3,5,5,2,6,5,5,4,5,4,5,4,2,6,4,6,6,5,6
%N 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.
%C 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.
%C A072420 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.
%D A072420 M. J. Halm, TOSCOD, Mpossibilities 67, p. 2 (Sept. 1998)
%H A072420 Sean A. Irvine, <a href="/A072420/b072420.txt">Table of n, a(n) for n = 1..1000</a>
%H A072420 M. J. Halm, <a href="http://michaelhalm.tripod.com/andre_joyce_s_coined_words.htm">Joycesquean neologisms</a>
%H A072420 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a072/A072420.java">Java program</a> (github)
%F A072420 By applying the proper combination of the two alternative operations one minimum number of operations can be determined.
%e A072420 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.
%Y A072420 Cf. A006577.
%K A072420 nonn,base
%O A072420 1,1
%A A072420 _Michael Joseph Halm_, Jul 31 2002
%E A072420 a(31) onward corrected by _Sean A. Irvine_, Sep 29 2024