login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146088 Numbers n with the property that shifting the rightmost digit of n to the left end doubles the number. 5
0, 105263157894736842, 157894736842105263, 210526315789473684, 263157894736842105, 315789473684210526, 368421052631578947, 421052631578947368, 473684210526315789, 105263157894736842105263157894736842, 157894736842105263157894736842105263 (list; graph; refs; listen; history; text; internal format)
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^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

LINKS

Table of n, a(n) for n=0..10.

G. P. Michon, Deriving A146088 from linear decadic equations.

FORMULA

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.

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 cross-references 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}] (* Jean-Fran├žois Alcover, Jan 16 2013, after M. F. Hasler *)

PROG

(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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 28 18:26 EDT 2017. Contains 285579 sequences.