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Search: id:A117057
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| A117057 |
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Palindromes which are divisible by the product of their digits. |
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+0
2
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 111, 212, 1111, 2112, 4224, 11111, 11711, 13131, 21112, 21312, 31113, 42624, 111111, 211112, 234432, 1111111, 1113111, 2111112, 2112112, 2114112, 2118112, 11111111, 21111112, 21122112, 61111116, 111111111
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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4224 is in the sequence because (1) it is a palindrome, (2) the product of its digits is 4*2*2*4=64 and 4224 is divisible by 64.
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MATHEMATICA
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fQ[n_] := Block[{id = IntegerDigits@n}, Reverse@id == id && Count[id, 0] == 0 && Mod[n, Times @@ id] == 0]; Do[ If[ fQ@n, Print@n], {n, 10^7}] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) {m=120000000; for(n=1, m, k=n; rev=0; while(k>0, d=divrem(k, 10); k=d[1]; rev=10*rev+d[2]); if(n==rev, p=1; h=n; while(h>0, d=divrem(h, 10); h=d[1]; p=p*d[2]); if(p>0&&n%p==0, print1(n, ", "))))} - (Klaus Brockhaus)
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CROSSREFS
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Cf. A002113.
Sequence in context: A167152 A064704 A083136 this_sequence A029967 A029968 A097855
Adjacent sequences: A117054 A117055 A117056 this_sequence A117058 A117059 A117060
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
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EXTENSIONS
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a(23) to a(36) from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 17 2006
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