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A230004
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Numbers n such that phi(n) + sigma(n) = reversal(n) + 4.
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6
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OFFSET
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1,1
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COMMENTS
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If p=5*10^m-1 is prime (m is a term of A056712) then p is in the sequence.
Let p(m,n) = 10^(m+3)*(7*10^(m+2)+92)*(10^((m+4)*n)-1)/(10^(m+4)-1) +7*10^(m+1)+9, if m>0, n>=0 and p(m,n) is prime then 4*p(m,n) is in the sequence.
All known terms are of these two forms.
What is the smallest term of the sequence which is not of the form p or 4*p where p is prime?
Note that a(2)=4*p(1,0), a(5)=4*p(3,0), a(7)=4*p(5,0) and a(8)=4*p(1,1).
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LINKS
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EXAMPLE
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phi(499)+sigma(499) = 498+500 = 994+4 = reversal(499)+4, so 499 is in the sequence.
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MATHEMATICA
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r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[If[DivisorSigma[1, n] + EulerPhi[n] == r[n] + 4, Print[n]], {n, 1050000000}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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