

A146088


Numbers n with the property that shifting the rightmost digit of n to the left end doubles the number.


10



0, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 105263157894736842105263157894736842, 157894736842105263157894736842105263
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OFFSET

0,2


COMMENTS

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^d2), i.e. 10^d=2 (mod 19) and n = m(10^d2)/19, m=2..9 (to ensure that n has d digits). Thus for each d = 18j1, j=1,2,3... we have exactly 8 solutions which are the jfold 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


LINKS

Table of n, a(n) for n=0..10.
G. P. Michon, Deriving A146088 from linear decadic equations.


FORMULA

a(n) = ((10^d2)/19*10+1)m, where m=(n1)%8+2 is the trailing digit and d=(n+7)\8*181 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.


EXAMPLE

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 crossreferences within OEIS (e.g., A217592) or outside of it.
a(4) = 263157894736842105 because 2*a(4) = 526315789473684210.


MATHEMATICA

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}] (* JeanFrançois Alcover, Jan 16 2013, after M. F. Hasler *)


PROG

(PARI) A146088(n) = ((10^((n+7)\8*181)2)/19*10+1)*((n1)%8+2)
/* or a more experimental approach: */ for(d=1, 99, Mod(10, 19)^k2 & next; for(m=2, 9, print1(", ", m*(10^k2)/19, m))) \\\\ M. F. Hasler, May 04 2009


CROSSREFS

Cf. A092697, A146561, A146569, A146754, A217592.
Sequence in context: A104837 A008923 A267076 * A217592 A092697 A097717
Adjacent sequences: A146085 A146086 A146087 * A146089 A146090 A146091


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, based on correspondence from William A. Hoffman III (whoff(AT)robill.com), Apr 10 2009


EXTENSIONS

More terms from M. F. Hasler, May 04 2009
a(0)=0 added by G. P. Michon, Oct 29 2012


STATUS

approved



