A291321 Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 8.

1012658227848, 1139240506329, 10126582278481012658227848, 11392405063291139240506329, 101265822784810126582278481012658227848, 113924050632911392405063291139240506329, 1012658227848101265822784810126582278481012658227848

Offset: 1

Author

Seiichi Manyama, Aug 22 2017

Keywords

• nonn
• base
• easy

Comments

Let x = (10^12 - 8)/79 = 12658227848. Then a(1) = 8*x*10 + 8, a(2) = 9*x*10 + 9.

For consistency with A146088 (similar for ratio k=2) and others, where an initial a(0) = 0 has been added, the same could be considered here. It would be compatible with the formula given for a(2k). - M. F. Hasler, May 03 2025

Examples

			a(1) = b*10 + 8 with b = 101265822784, and 8*a(1) = 8101265822784 = 8*10^12 + b.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..152
• Wikipedia, Parasitic number.

Crossrefs

Cf. A146088 (k=2), A146561 (k=3), A146569 (k=4), A146754 (k=5), A291354 (k=6), A291215 (k=7), this sequence (k=8), A291353 (k=9).

All these are subsequences of A034089 (except for an initial 0 in some of them).

Cf. A092697, A097717.

Programs

PARI

a(n)=10^((n+1)\2*13)\79*(9-n%2) \\ Charles R Greathouse IV, Aug 23 2017

Formula

a(2*k - 1) = 8*(10^(13*k) - 1)/79.

a(2*k) = 9*(10^(13*k) - 1)/79.

Extensions

Edited by M. F. Hasler, May 03 2025