cp's OEIS Frontend

A351876 Numbers whose trajectory under iteration of the product of cubes of nonzero digits map includes 1 (conjectured).

%I A351876 #27 Mar 09 2022 10:52:41
%S A351876 1,2,3,5,8,10,11,12,13,15,18,20,21,24,25,27,30,31,42,45,50,51,52,54,
%T A351876 55,56,57,65,72,75,80,81,100,101,102,103,105,108,110,111,112,113,115,
%U A351876 118,120,121,124,125,127,130,131,142,145,150,151,152,154,155,156,157,165,172,175,180,181
%N A351876 Numbers whose trajectory under iteration of the product of cubes of nonzero digits map includes 1 (conjectured).
%C A351876 To determine whether a given number k is a term of this sequence, start with k, take the cube of the product of its nonzero digits, apply the same process to the result, and continue until 30 iterations are reached. If 1 is reached during the process, k is a term of this sequence. If not, k is not a term of this sequence.
%C A351876 Every power 10^k is a term of this sequence.
%C A351876 If k is a term, the numbers obtained by inserting zeros anywhere in k are terms.
%C A351876 If k is a term, the numbers obtained by inserting ones anywhere in k are terms.
%C A351876 If k is a term, each distinct permutation of the digits of k gives another term.
%C A351876 If k is a term, the number of iterations required to converge to 1 is less than or equal to 10 (conjectured).
%e A351876 217 is a term of the sequence; its trajectory is 217 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1.
%e A351876 4 is not a term of the sequence; its trajectory begins with 4 -> 64 -> 13824 -> 7077888 -> 5416169448144896 -> 188436971148778297205194752000 -> 1545896640285238037724131582088286996267008000000 -> ... Subsequent terms in the trajectory get larger and larger, rather than reaching 1. However, it is not yet known whether it eventually reaches 1 after some number of iterations > 30.
%t A351876 Select[Range[1000], FixedPoint[ Product[ReplaceAll[0 -> 1][IntegerDigits[#]][[i]]^3, {i, 1, Length[ReplaceAll[0 -> 1][IntegerDigits[#]]]}] &, #, 12] == 1 &]
%Y A351876 Cf. A351327, A051801.
%Y A351876 Cf. A352172 (product of cubes of nonzero digits).
%K A351876 nonn,base
%O A351876 1,2
%A A351876 _Luca Onnis_, Feb 23 2022