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

142857, 142857142857, 142857142857142857, 142857142857142857142857, 142857142857142857142857142857, 142857142857142857142857142857142857, 102040816326530612244897959183673469387755, 122448979591836734693877551020408163265306, 142857142857142857142857142857142857142857

Offset

1,1

Comments

From Seiichi Manyama, Aug 22 2017: (Start)

For k >= 1, (10^(6*k) - 1)/7 is a term.

For 5 <= a <= 9 and k >= 1, a*(10^(42*k) - 1)/49 is a term. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..258

Wikipedia, Parasitic number.

Example

From Seiichi Manyama, Aug 22 2017: (Start)
b1 = 14285.
a(1) = b1*10 + 7,
5*a(1) = 714285 = 7*10^5 + b1.
b7 = 10204081632653061224489795918367346938775.
a(7) = b7*10 + 5,
5*a(7) = 510204081632653061224489795918367346938775 = 5*10^41 + b7. (End)

Maple

f:= proc(d) # solutions with d+1 digits
    local b, R, a;
    R:= NULL;
    for b from ceil(49*10^(d-1)/(10^d - 1)) to 9 do
       a:= (10^d-5)*b/49;
       if a::integer then R:= R, 10*a+b fi
    od;
   R
end proc:
map(f, [$1..42]); # Robert Israel, Nov 05 2024

Crossrefs

Cf. A146088 (k=2), A146561 (k=3), A146569 (k=4), this sequence (k=5), A291215 (k=7).

Cf. A092697, A097717.

Sequence in context: A306265 A144504 A344436 * A180340 A004042 A145742

Adjacent sequences: A146751 A146752 A146753 * A146755 A146756 A146757

Keyword

nonn,base

Author

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

Status

approved