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Search: id:A101702
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| A101702 |
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Numbers n such that the sum of the factorials of their digits is equal to the reversal of n. |
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| 1, 2, 541, 52100, 58504, 66410, 430000, 863180, 8601400, 17927300, 27927300, 31000000, 665100000, 3715000000, 6739630000, 11000000000, 21000000000, 53100000000, 70858000000, 79637300000, 451000000000, 1715000000000, 2715000000000, 48304000000000, 340000000000000, 5520000000000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next term is greater than 8*10^8. If s=sum of the factorials of digits of n & reversal(n)>=s then 10^(reversal(n)-s)*n is in the sequence. Example n=23; s=2!+3!; reversal(23)-s=24 & 23*10^24 is in the sequence. So this sequence is infinite because there exists infinitely many numbers n such that reversal(n)>s. If n is a k-digit term of this sequence and the first digit of n is 1 then 10^(k-1)+n is also in the sequence. Examples : n=1 so 10^(1-1)+1=2 is in the sequence, n=17927300 so 10^7+17927300=27927300 is in the sequence. If n>5 then 10 divides a(n). If 10 doesn't divide a(n) then the reversal of n is in the sequence A010480, so all terms of A010480 are : reversal(1), reversal(2), reversal(541) & reversal(58504).
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EXAMPLE
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665100000 is in the sequence because reversal(665100000)=1566=
6!+6!+5!+1!+0!+0!+0!+0!+0!.
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MATHEMATICA
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Do[h = FactorInteger[n]; l = Length[h]; If[FromDigits[Reverse[IntegerDigits[n] == Sum[h[[k]]], {k, l}], Print[n]], {n, 800000000}]
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CROSSREFS
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Cf. A014080, A049529, A101697.
Sequence in context: A080778 A007513 A071613 this_sequence A119780 A120840 A058429
Adjacent sequences: A101699 A101700 A101701 this_sequence A101703 A101704 A101705
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KEYWORD
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base,nonn
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AUTHOR
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Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Dec 24 2004
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EXTENSIONS
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More terms from Donovan Johnson (donovan.johnson(AT)yahoo.com), Feb 26 2008
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