1,1

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. No further term up to 10^9.

253782 is in the sequence because reversal(253782)=287352; sigma(253782)=574704 & 2*287352=574704.

reversal[n_]:= FromDigits[Reverse[IntegerDigits[n]]]; Do[If[2* reversal[n]== DivisorSigma[1, n], Print[n]], {n, 1000000000}]

Cf. A093170, A096507, A099190, A105322, A105323, A105325, A105326.

Sequence in context: A006585 A008562 A041063 this_sequence A041060 A089926 A135594

Adjacent sequences: A105321 A105322 A105323 this_sequence A105325 A105326 A105327

base,more,nonn

Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Apr 16 2005