cp's OEIS Frontend

A146754 Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 5.

%I A146754 #34 May 06 2025 10:59:50
%S A146754 142857,142857142857,142857142857142857,142857142857142857142857,
%T A146754 142857142857142857142857142857,142857142857142857142857142857142857,
%U A146754 102040816326530612244897959183673469387755,122448979591836734693877551020408163265306,142857142857142857142857142857142857142857
%N A146754 Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 5.
%C A146754 From _Seiichi Manyama_, Aug 22 2017: (Start)
%C A146754 For k >= 1, (10^(6*k) - 1)/7 is a term.
%C A146754 For 5 <= a <= 9 and k >= 1, a*(10^(42*k) - 1)/49 is a term. (End)
%C A146754 For consistency with A146088 (similar for ratio 2), where an initial a(0) = 0 has been added, the same could be considered here. It would be compatible with the formulas given above (with k = 0). - _M. F. Hasler_, May 03 2025
%H A146754 Robert Israel, <a href="/A146754/b146754.txt">Table of n, a(n) for n = 1..258</a>
%H A146754 Wikipedia, <a href="https://en.wikipedia.org/wiki/Parasitic_number">Parasitic number</a>.
%e A146754 From _Seiichi Manyama_, Aug 22 2017: (Start)
%e A146754 a(1) = b1*10 + 7 with b1 = 14285, and 5*a(1) = 714285 = 7*10^5 + b1.
%e A146754 a(7) = b7*10 + 5 with b7 = 10204081632653061224489795918367346938775, and
%e A146754   5*a(7) = 510204081632653061224489795918367346938775 = 5*10^41 + b7. (End)
%p A146754 f:= proc(d) # solutions with d+1 digits
%p A146754     local b,R,a;
%p A146754     R:= NULL;
%p A146754     for b from ceil(49*10^(d-1)/(10^d - 1)) to 9 do
%p A146754        a:= (10^d-5)*b/49;
%p A146754        if a::integer then R:= R, 10*a+b fi
%p A146754     od;
%p A146754    R
%p A146754 end proc:
%p A146754 map(f, [$1..42]); # _Robert Israel_, Nov 05 2024
%Y A146754 Cf. A146088 (k=2), A146561 (k=3), A146569 (k=4), this sequence (k=5), A291354 (k=6), A291215 (k=7), A291321 (k=8), A291353 (k=9).
%Y A146754 All these are subsequences of A034089 (except for an initial 0 in some of them).
%Y A146754 Cf. A092697, A097717.
%K A146754 nonn,base
%O A146754 1,1
%A A146754 _N. J. A. Sloane_, based on correspondence from William A. Hoffman III (whoff(AT)robill.com), Apr 10 2009