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A344749
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Numbers m with decimal expansion (d_k, ..., d_1) such that d_i = m ^ i mod 10 for i = 1..k.
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3
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 19, 42, 48, 55, 64, 66, 93, 97, 111, 248, 397, 464, 555, 666, 793, 842, 919, 1111, 1397, 1793, 1919, 5555, 6248, 6464, 6666, 6842, 11111, 26842, 31793, 46464, 55555, 66666, 71397, 86248, 91919, 111111, 191919, 426842, 486248
(list;
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listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Positive terms are zeroless (A052382) and uniquely determined by their final digit (A010879) and the number of digits in their decimal expansion (A055642).
If m belongs to the sequence, then A217657(m) also belongs to the sequence.
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LINKS
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EXAMPLE
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- 7^1 = 7 mod 10,
- 7^2 = 9 mod 10,
- 7^3 = 3 mod 10,
- 7^4 = 1 mod 10,
- so 1397 belongs to the sequence.
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PROG
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(PARI) is(n) = { my (r=n); for (k=1, oo, if (r==0, return (1), (n^k)%10!=r%10, return (0), r\=10)) }
(PARI) print (setbinop((d, k) -> sum(i=1, k, 10^(i-1) * ((d^i)%10)), [1..9], [0..7])[1..50])
(Python)
def ok(m):
d = str(m)
return all(d[-i] == str((m**i)%10) for i in range(1, len(d)+1))
(Python)
def auptod(maxdigits):
alst = [0]
for k in range(1, maxdigits+1):
aklst = []
for d1 in range(1, 10):
d = [(d1**i)%10 for i in range(k, 0, -1)]
aklst.append(int("".join(map(str, d))))
alst.extend(sorted(aklst))
return alst
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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