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A344749 Numbers m with decimal expansion (d_k, ..., d_1) such that d_i = m ^ i mod 10 for i = 1..k.

%I A344749 #21 May 31 2021 02:11:14
%S A344749 0,1,2,3,4,5,6,7,8,9,11,19,42,48,55,64,66,93,97,111,248,397,464,555,
%T A344749 666,793,842,919,1111,1397,1793,1919,5555,6248,6464,6666,6842,11111,
%U A344749 26842,31793,46464,55555,66666,71397,86248,91919,111111,191919,426842,486248
%N A344749 Numbers m with decimal expansion (d_k, ..., d_1) such that d_i = m ^ i mod 10 for i = 1..k.
%C A344749 Positive terms are zeroless (A052382) and uniquely determined by their final digit (A010879) and the number of digits in their decimal expansion (A055642).
%C A344749 If m belongs to the sequence, then A217657(m) also belongs to the sequence.
%H A344749 Rémy Sigrist, <a href="/A344749/b344749.txt">Table of n, a(n) for n = 1..2251</a>
%e A344749 - 7^1 = 7 mod 10,
%e A344749 - 7^2 = 9 mod 10,
%e A344749 - 7^3 = 3 mod 10,
%e A344749 - 7^4 = 1 mod 10,
%e A344749 - so 1397 belongs to the sequence.
%o A344749 (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 A344749 (PARI) print (setbinop((d,k) -> sum(i=1, k, 10^(i-1) * ((d^i)%10)), [1..9], [0..7])[1..50])
%o A344749 (Python)
%o A344749 def ok(m):
%o A344749   d = str(m)
%o A344749   return all(d[-i] == str((m**i)%10) for i in range(1, len(d)+1))
%o A344749 print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, May 29 2021
%o A344749 (Python)
%o A344749 def auptod(maxdigits):
%o A344749   alst = [0]
%o A344749   for k in range(1, maxdigits+1):
%o A344749     aklst = []
%o A344749     for d1 in range(1, 10):
%o A344749       d = [(d1**i)%10 for i in range(k, 0, -1)]
%o A344749       aklst.append(int("".join(map(str, d))))
%o A344749     alst.extend(sorted(aklst))
%o A344749   return alst
%o A344749 print(auptod(6)) # _Michael S. Branicky_, May 29 2021
%Y A344749 Cf. A010879, A052382, A055642, A217657, A344555, A344748, A344822.
%K A344749 nonn,base,easy
%O A344749 1,3
%A A344749 _Rémy Sigrist_, May 28 2021