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%I #19 May 31 2021 02:11:11
%S 0,1,2,3,4,5,6,7,8,9,21,26,42,47,63,68,84,89,147,284,321,468,505,642,
%T 789,826,963,2468,2963,4321,4826,6284,6789,8147,8642,50505,52963,
%U 54321,56789,58147,208642,258147,406284,456789,604826,654321,802468,852963
%N Numbers m with decimal expansion (d_k, ..., d_1) such that d_i = m * i mod 10 for i = 1..k.
%C Positive terms have no trailing zero in decimal representation (A067251), and are uniquely determined by their final digit d (A010879) and the number of digits, say k, in their decimal expansion (A055642); d*k cannot be a multiple of 10.
%C If m belongs to the sequence, then A217657(m) also belongs to the sequence.
%H Rémy Sigrist, <a href="/A344748/b344748.txt">Table of n, a(n) for n = 1..1826</a>
%e - 6 * 1 = 6 mod 10,
%e - 6 * 2 = 2 mod 10,
%e - 6 * 3 = 8 mod 10,
%e - 6 * 4 = 4 mod 10,
%e - so 4826 belongs to the sequence.
%o (PARI) is(n) = { my (r=n); for (k=1, oo, if (r==0, return (1), (n*k)%10!=r%10, return (0), r\=10)) }
%o (PARI) print (setbinop((d,k) -> sum(i=1, k, 10^(i-1) * ((d*i)%10)), [1..9], [0..6]))
%o (Python)
%o def ok(m):
%o d = str(m)
%o return all(d[-i] == str((m*i)%10) for i in range(1, len(d)+1))
%o print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, May 29 2021
%o (Python)
%o def auptod(maxdigits):
%o alst = [0]
%o for k in range(1, maxdigits+1):
%o aklst = []
%o for d1 in range(1, 10):
%o d = [(d1*i)%10 for i in range(k, 0, -1)]
%o if d[0] != 0: aklst.append(int("".join(map(str, d))))
%o alst.extend(sorted(aklst))
%o return alst
%o print(auptod(6)) # _Michael S. Branicky_, May 29 2021
%Y Cf. A010879, A055642, A067251, A217657, A344749, A344822.
%K nonn,base,easy
%O 1,3
%A _Rémy Sigrist_, May 28 2021
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