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A146088
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Numbers n with the property that shifting the rightmost digit of n to the left end doubles the number.
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10
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0, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 105263157894736842105263157894736842, 157894736842105263157894736842105263
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OFFSET
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0,2
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COMMENTS
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The sequence is infinite, since repeating 105263157894736842 any number of times (e.g. 105263157894736842105263157894736842) gives another number with the same property.
A number N = 10n+m is in the sequence iff 2N = m*10^d+n, where d is the number of digits of n = [N/10]. This is equivalent to 19n = m(10^d-2), i.e. 10^d=2 (mod 19) and n = m(10^d-2)/19, m=2..9 (to ensure that n has d digits). Thus for each d = 18j-1, j=1,2,3... we have exactly 8 solutions which are the j-fold repetition of one among {a(1),...,a(8)}. - M. F. Hasler, May 04 2009
Normally lists have offset 1, but there are good reasons to make an exception in this case. - N. J. A. Sloane, Dec 24 2012
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LINKS
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Table of n, a(n) for n=0..10.
G. P. Michon, Deriving A146088 from linear decadic equations.
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FORMULA
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a(n) = ((10^d-2)/19*10+1)m, where m=(n-1)%8+2 is the trailing digit and d=(n+7)\8*18-1 is the number of other digits. - M. F. Hasler, May 04 2009
a(8k+i) = A217592(9k+i+1)/2 for i=1..8 with any k.
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EXAMPLE
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The sequence starts with a(0)=0 because rotating a lone 0 does double 0. That initial trivial term was not given an index of 1 when it was added, so that the index of other terms of A146088 would not change and invalidate delicate prior cross-references within OEIS (e.g., A217592) or outside of it.
a(4) = 263157894736842105 because 2*a(4) = 526315789473684210.
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MATHEMATICA
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a[n_] := (m = Mod[n - 1, 8] + 2; d = Floor[(n + 7)/8]*18 - 1; ((10/19)*(10^d - 2) + 1)*m); Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Jan 16 2013, after M. F. Hasler *)
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PROG
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(PARI) A146088(n) = ((10^((n+7)\8*18-1)-2)/19*10+1)*((n-1)%8+2)
/* or a more experimental approach: */ for(d=1, 99, Mod(10, 19)^k-2 & next; for(m=2, 9, print1(", ", m*(10^k-2)/19, m))) \\\\ M. F. Hasler, May 04 2009
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CROSSREFS
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Cf. A092697, A146561, A146569, A146754, A217592.
Sequence in context: A104837 A008923 A267076 * A217592 A092697 A097717
Adjacent sequences: A146085 A146086 A146087 * A146089 A146090 A146091
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, based on correspondence from William A. Hoffman III (whoff(AT)robill.com), Apr 10 2009
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EXTENSIONS
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More terms from M. F. Hasler, May 04 2009
a(0)=0 added by G. P. Michon, Oct 29 2012
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STATUS
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approved
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