## Number 9182736455463728191

$9182736455463728191 = 23 \times 4093 \times 8779 \times 21649 \times 513239$

$918273645 \; || \; 546372819 \; || \; 1$

Producing palindromes:

$9182736455463728191 \times 11 = 101010101010101010101$
$9182736455463728191 \times 11^2 = 1111111111111111111111$
$9182736455463728191 \times 11^3 = 12222222222222222222221$
$9182736455463728191 \times 11^4 = 134444444444444444444431$
$9182736455463728191 \times 11^5 = 1478888888888888888888741$

The pattern breaks:

$9182736455463728191 \times 11^6 = 16267777777777777777776151$
$9182736455463728191 \times 11^7 = 178945555555555555555537661$
$9182736455463728191 \times 11^8 = 1968401111111111111110914271$
$9182736455463728191 \times 11^9 = 21652412222222222222220056981$

The repeated digits in the middle are slowing diminishing:

$9182736455463728191 \times 11^{10} = 238176534444444444444420626791$
$9182736455463728191 \times 11^{11} = 2619941878888888888888626894701$
$9182736455463728191 \times 11^{12} = 28819360667777777777774895841711$
$9182736455463728191 \times 11^{13} = 317012967345555555555523854258821$
$9182736455463728191 \times 11^{14} = 3487142640801111111110762396847031$
$9182736455463728191 \times 11^{15} = 38358569048812222222218386365317341$
$9182736455463728191 \times 11^{16} = 421944259536934444444402250018490751$
$9182736455463728191 \times 11^{17} = 4641386854906278888888424750203398261$
$9182736455463728191 \times 11^{18} = 51055255403969067777772672252237380871$
$9182736455463728191 \times 11^{19} = 561607809443659745555499394774611189581$
$9182736455463728191 \times 11^{20} = 6177685903880257201110493342520723085391$
$9182736455463728191 \times 11^{21} = 67954544942682829212215426767727953939301$

These results show that only digits 1, 2, 4, 5, 7, 8 are repeated in the middle of each number.

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## About benvitalis

math grad - Interest: Number theory
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