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 A351876 Numbers whose trajectory under iteration of the product of cubes of nonzero digits map includes 1 (conjectured). 10
 1, 2, 3, 5, 8, 10, 11, 12, 13, 15, 18, 20, 21, 24, 25, 27, 30, 31, 42, 45, 50, 51, 52, 54, 55, 56, 57, 65, 72, 75, 80, 81, 100, 101, 102, 103, 105, 108, 110, 111, 112, 113, 115, 118, 120, 121, 124, 125, 127, 130, 131, 142, 145, 150, 151, 152, 154, 155, 156, 157, 165, 172, 175, 180, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. Every power 10^k is a term of this sequence. If k is a term, the numbers obtained by inserting zeros anywhere in k are terms. If k is a term, the numbers obtained by inserting ones anywhere in k are terms. If k is a term, each distinct permutation of the digits of k gives another term. If k is a term, the number of iterations required to converge to 1 is less than or equal to 10 (conjectured). LINKS Table of n, a(n) for n=1..65. EXAMPLE 217 is a term of the sequence; its trajectory is 217 -> 2744 -> 11239424 -> 5159780352 -> 54010152000000000 -> 8000000 -> 512 -> 1000 -> 1. 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. MATHEMATICA Select[Range[1000], FixedPoint[ Product[ReplaceAll[0 -> 1][IntegerDigits[#]][[i]]^3, {i, 1, Length[ReplaceAll[0 -> 1][IntegerDigits[#]]]}] &, #, 12] == 1 &] CROSSREFS Cf. A351327, A051801. Cf. A352172 (product of cubes of nonzero digits). Sequence in context: A272669 A028770 A321702 * A028800 A028841 A028840 Adjacent sequences: A351873 A351874 A351875 * A351877 A351878 A351879 KEYWORD nonn,base AUTHOR Luca Onnis, Feb 23 2022 STATUS approved

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Last modified August 10 12:34 EDT 2024. Contains 375056 sequences. (Running on oeis4.)