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Search: id:A088797
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| A088797 |
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Numbers n such that n divides the concatenation of n-2 and n-1. |
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+0
13
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| 3, 7, 67, 667, 6667, 66667, 666667, 2857143, 6666667, 66666667, 666666667, 1052631579, 6666666667, 66666666667, 666666666667, 2857142857143, 6666666666667, 11764705882353, 66666666666667, 666666666666667
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OFFSET
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1,1
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COMMENT
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For a 10-digit number, the difference between cat((n+2),(n+1)) and cat ((n-2),(n-1)) is 40000000002 (as long as n-2 to n+2 are all numbers with the same number of digits). This difference has only 3 divisors which are ten digits long (1052631579, 2105263158 and 6666666667) of which two belong to the sequence. As 40000000002 has no other 10-digit factors, it is necessary to consider 11-digit numbers to obtain more terms.
All numbers of the form 2(10^n-1)/3+1 are members. - Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 21 2003 & Oct 28 2003
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EXAMPLE
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a(2)=7 because (7-2) concatenated with (7-1) yields 56 and 7 is a divisor of 56. a(4)=667 because 667 is a divisor of 665666.
10526315771052631578/1052631579 = 9999999982.
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MATHEMATICA
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Select[ Range[8250000000], Mod[ FromDigits[ Join[ IntegerDigits[ # - 2], IntegerDigits[ # - 1]]], # ] == 0 &]
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CROSSREFS
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Cf. A069860, A069862, A069871, A088798.
Sequence in context: A110433 A041817 A120364 this_sequence A165589 A127177 A127179
Adjacent sequences: A088794 A088795 A088796 this_sequence A088798 A088799 A088800
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 18 2003
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 21 2003
Further terms from Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 29 2003
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