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A344822 Numbers m with decimal expansion (d_1, ..., d_k) such that d_i = m * i mod 10 for i = 1..k.

%I A344822 #12 May 31 2021 02:11:17
%S A344822 0,1,2,3,4,5,6,7,8,9,505,50505,246802,482604,628406,864208,5050505,
%T A344822 505050505,12345678901,24680246802,36925814703,48260482604,
%U A344822 50505050505,62840628406,74185296307,86420864208,98765432109,5050505050505,505050505050505,2468024680246802
%N A344822 Numbers m with decimal expansion (d_1, ..., d_k) such that d_i = m * i mod 10 for i = 1..k.
%C A344822 This sequence is infinite as it contains 5 * A094028(k) for any k > 0.
%C A344822 Also contains terms with patterns 2(46802)^k, 4(82604)^k, 6(28406)^k, 8(64208)^k, 1(2345678901)^k, 3(6925814703)^k, 7(4185296307)^k, 9(8765432109)^k for k >= 0, where ^ denotes repeated concatenation; all terms have first and last digits the same. - _Michael S. Branicky_, May 29 2021
%H A344822 Rémy Sigrist, <a href="/A344822/b344822.txt">Table of n, a(n) for n = 1..426</a>
%H A344822 Rémy Sigrist, <a href="/A344822/a344822.gp.txt">PARI program for A344822</a>
%e A344822 - 4 * 1 = 4 mod 10,
%e A344822 - 4 * 2 = 8 mod 10,
%e A344822 - 4 * 3 = 2 mod 10,
%e A344822 - 4 * 4 = 6 mod 10,
%e A344822 - 4 * 5 = 0 mod 10,
%e A344822 - 4 * 6 = 4 mod 10,
%e A344822 so 482604 is a term.
%o A344822 (PARI) is(n) = { my (d=digits(n)); for (k=1, #d, if (d[k] != (n*k)%10, return (0))); return (1) }
%o A344822 (PARI) See Links section.
%o A344822 (Python)
%o A344822 def ok(m):
%o A344822   d = str(m)
%o A344822   return all(d[i-1] == str((m*i)%10) for i in range(1, len(d)+1))
%o A344822 print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, May 29 2021
%o A344822 (Python)
%o A344822 def auptod(maxdigits):
%o A344822   alst = [0]
%o A344822   for k in range(1, maxdigits+1):
%o A344822     for d1 in range(1, 10):
%o A344822       d = [(d1*i)%10 for i in range(1, k+1)]
%o A344822       if d1 == d[-1]: alst.append(int("".join(map(str, d))))
%o A344822   return alst
%o A344822 print(auptod(16)) # _Michael S. Branicky_, May 29 2021
%Y A344822 Cf. A094028, A344748, A344823.
%K A344822 nonn,base
%O A344822 1,3
%A A344822 _Rémy Sigrist_, May 29 2021