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A328142 Elements of cycles for iterations of A329623: n -> |n - concat(sum of adjacent digits of n)|. 5
1, 2, 3, 4, 5, 6, 7, 8, 9, 182, 273, 364, 455, 546, 637, 728, 1728, 2637, 3546, 4455, 5364, 6273, 7182, 17182, 26273, 35364, 44455, 53546, 62637, 71728, 171728, 262637, 353546, 444455, 535364, 626273, 717182, 1717182, 2626273, 3535364, 4444455, 5353546, 6262637, 7171728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equivalently: range of A328865 \ {-1}.

By a k-cycle (or cycle of length k) of A329623 we mean a vector (x_1, ..., x_k) such that A329623(x_i) = x_{i+1} for i < k, and A329623(x_k) = x_1. We include here the cycles of length k = 1 which are the fixed points of A329623, viz A329623(x_1) = x_1. No cycle with k > 2 is known.

There are 7 infinite subsequences: for initial digit 1 <= d <= 7, alternate digit d and 8-d to form an undulating (A033619) number of arbitrary length L >= 3, then add 11.

The terms with initial digit d > 4 are the larger member of a 2-cycle having a term with d < 4 as smaller member. The terms with d = 4 (and those <= 9) are fixed points. So far no other fixed points or other cycles are known. As far as this remains valid, the terms of this sequence are characterized by A329623(A329623(x)) = x.

Sequence A328279 lists the smallest member of each cycle.

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

The single-digit numbers 1, ..., 9 and the numbers f(k) = 4*(10^k-1)/9 + 11, k >= 3, are fixed points of A329623.

Indeed, for f(k) = 4...455 we have A053392(f(k)) = 8...910 = 2*f(k), so A329623(f(k)) = 2*f(k) - f(k) = f(k).

For a(10) = 182, we have A329623(182) = 728 and A329623(728) = 182, so these are members of the 2-cycle (182, 728).

For a(11) = 273, we have A329623(273) = 637 and A329623(637) = 273, so these are members of the 2-cycle (273, 637).

Similarly for all subsequent terms except the f(k) of the form 4...455.

PROG

(PARI) apply( {A328142(n)=if(n>9, fromdigits(vector((n+8)\/7, i, n=if(i>1, 8-n, (n+4)%7+1)))+11, n)}, [1..40]) \\ As far as there are no other terms than those described in COMMENTS. - M. F. Hasler, Dec 06 2019, replacing earlier code.

CROSSREFS

Cf. A329623, A053392 (concatenate sums of adjacent digits of n), A328865, A329624.

See A328279 for the smallest representative of each cycle.

Sequence in context: A032569 A343036 A254960 * A328279 A039723 A002998

Adjacent sequences:  A328139 A328140 A328141 * A328143 A328144 A328145

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Dec 02 2019

STATUS

approved

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Last modified June 25 10:04 EDT 2022. Contains 354844 sequences. (Running on oeis4.)