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A105324
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Numbers n such that 2*reversal(n)=sigma(n).
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6
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6, 73, 483, 4074, 4473, 4623, 7993, 42813, 69855, 253782, 799993, 7999993, 46000023, 426000213, 4600000023, 6718967838, 42600000213, 46000000023, 79999999993, 426000000213
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OFFSET
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1,1
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COMMENTS
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I. If p=8*10^n-7 is a prime then p is in the sequence because reversal(p)=4*10^n-3 & sigma(p)=8*10^n-6 so 2*reversal(p) =sigma(p). 73,7993,799993 & 7999993 are such terms.
II. If q=(2*10^n+1)/3 is a prime then (a): 69*q is in the sequence because 69*q=46*10^n+23; reversal (69*q)=32*10^n+64 & sigma(69*q)=96*q+96=64*10^n+128 so 2*reversal (69*q)=sigma(69*q). 483,4623 & 46000023 are such terms. (b): 639*q is in the sequence because 639*q=426*10^n+213; reversal (639*q)=312*10^n+624 & sigma(639*q)=936*q+936=624*10^n+1248 so 2*reversal(639*q)=sigma(639*q). 42813 & 426000213 are such terms.
a(21) > 10^12. - Giovanni Resta, Oct 28 2012
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LINKS
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Table of n, a(n) for n=1..20.
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EXAMPLE
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253782 is in the sequence because reversal(253782)=287352; sigma(253782)=574704 & 2*287352=574704.
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MATHEMATICA
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reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[2* reversal[n]== DivisorSigma[1, n], Print[n]], {n, 1000000000}]
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CROSSREFS
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Cf. A093170, A096507, A099190, A105322, A105323, A105325, A105326.
Sequence in context: A203433 A008562 A041063 * A179568 A202557 A041060
Adjacent sequences: A105321 A105322 A105323 * A105325 A105326 A105327
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KEYWORD
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base,more,nonn
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AUTHOR
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Farideh Firoozbakht, Apr 16 2005
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EXTENSIONS
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a(15)-a(19) from Donovan Johnson, Dec 21 2008
a(20) from Giovanni Resta, Oct 28 2012
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STATUS
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approved
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