This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A146088 #38 Aug 24 2025 16:33:51
%S A146088 0,105263157894736842,157894736842105263,210526315789473684,
%T A146088 263157894736842105,315789473684210526,368421052631578947,
%U A146088 421052631578947368,473684210526315789,105263157894736842105263157894736842,157894736842105263157894736842105263
%N A146088 Numbers k with the property that shifting the rightmost digit of k to the left end doubles the number.
%C A146088 The sequence is infinite, since repeating 105263157894736842 any number of times (e.g. 105263157894736842105263157894736842) gives another number with the same property.
%C A146088 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
%C A146088 Normally lists have offset 1, but there are good reasons to make an exception in this case. - _N. J. A. Sloane_, Dec 24 2012
%H A146088 Gerard P. Michon, <a href="http://www.numericana.com/answer/p-adic.htm#a146088">Deriving A146088 from linear decadic equations</a>.
%F A146088 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
%F A146088 a(8k+i) = A217592(9k+i+1)/2 for i=1..8 with any k.
%e A146088 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.
%e A146088 a(4) = 263157894736842105 because 2*a(4) = 526315789473684210.
%t A146088 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_ *)
%o A146088 (PARI) A146088(n) = ((10^((n+7)\8*18-1)-2)/19*10+1)*((n-1)%8+2)
%o A146088 /* 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
%Y A146088 Cf. A092697, A146561, A146569, A146754, A217592.
%Y A146088 Subsequence of A034089 (except for the initial 0).
%K A146088 nonn,base,changed
%O A146088 0,2
%A A146088 _N. J. A. Sloane_, based on correspondence from William A. Hoffman III (whoff(AT)robill.com), Apr 10 2009
%E A146088 More terms from _M. F. Hasler_, May 04 2009
%E A146088 a(0) = 0 added by _Gerard P. Michon_, Oct 29 2012