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Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 7.
6

%I #20 Aug 22 2017 03:23:13

%S 1014492753623188405797,1159420289855072463768,1304347826086956521739,

%T 10144927536231884057971014492753623188405797,

%U 11594202898550724637681159420289855072463768,13043478260869565217391304347826086956521739,101449275362318840579710144927536231884057971014492753623188405797

%N Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 7.

%C x = (10^21 - 7)/69 = 14492753623188405797.

%C a(1) = 7*x*10 + 7, a(2) = 8*x*10 + 8, a(3) = 9*x*10 + 9.

%H Robert Israel, <a href="/A291215/b291215.txt">Table of n, a(n) for n = 1..135</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Parasitic_number">Parasitic number</a>.

%F From _Robert Israel_, Aug 22 2017: (Start)

%F a(3k-2) = 7(10^(22k)-1)/69.

%F a(3k-1) = 8(10^(22k)-1)/69.

%F a(3k) = 9(10^(22k)-1)/69.

%F a(n+6) = (10^22+1) a(n+3) - 10^22 a(n).

%F G.f.: (1304347826086956521739*x^2 + 1159420289855072463768*x + 1014492753623188405797)/

%F (10^22*x^6 - (10^22+1)*x^3 + 1). (End)

%e b = 101449275362318840579.

%e a(1) = b*10 + 7,

%e 7*a(1) = 7101449275362318840579 = 7*10^21 + b.

%p seq(seq(y*((10^(22*k)-1)/69),y=7..9),k=1..6); # _Robert Israel_, Aug 22 2017

%Y Cf. A146088 (k=2), A146561 (k=3), A146569 (k=4), A146754 (k=5).

%Y Cf. A092697, A097717.

%K nonn,base

%O 1,1

%A _Seiichi Manyama_, Aug 21 2017