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Search: id:A130000
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| A130000 |
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Composite solutions to the equation reversal(x)-phi(x)=1 (*). |
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+0
3
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| 52, 1230, 5032, 5662, 10040, 14450, 56253, 56962, 58882, 92944, 564472, 731935, 1865170, 10882630, 102178040, 127648411
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A prime p is a solution of (*) iff p is a palindrome. A number of the form 38*(15*10^n-1) is in the sequence iff (15*10^n-1) is prime (the proof is easy).
The first three such terms are 38*(15*10^1-1), 38*(15*10^2-1) & 38*(15*10^15-1). There is no further term up to 3*10^9.
The sequence A130013 gives composite solutions of equation sigma(x)-reversal(x)=1 and the sequence A130031 gives composite solutions of equation phi(x)+sigma(x)=2*reversal(x).
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EXAMPLE
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reversal(127648411)-phi(127648411)=114846721-114846720=1 so 127648411 is in the sequence.
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MATHEMATICA
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r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[c=r[n]; If[c<n && c-EulerPhi[n]==1, Print[n]], {n, 2100000000}]
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CROSSREFS
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Cf. A130001, A130002, A130013, A130031.
Sequence in context: A007247 A083936 A133238 this_sequence A017768 A035721 A035798
Adjacent sequences: A129997 A129998 A129999 this_sequence A130001 A130002 A130003
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KEYWORD
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base,more,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 28 2007, Dec 03 2007
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