A230021 Numbers n such that sigma(n) = reversal(n+2).

21, 291, 2991, 43954, 211552, 439954, 43564354, 43999954, 464057476, 43999999954, 435600004354, 439560043954, 439999999954

Offset

1,1

Comments

If p=10^m-3 is prime then 3*p is in the sequence.

Let f(m,r)=22*((10^m-1)/(10^(m+2)-1))*(10^((m+2)r)-1)-1. If m>1 and p=f(m,r) is prime, then 2*p is in the sequence. a(11) > 2*10^11. - Giovanni Resta, Dec 13 2013

According to comments and known terms of A230768, the next three terms are 435600004354, 439560043954, 439999999954 and a(14)>10^12.

Let g(m,r,s) = 22*(10^(m+r+4)*(10^(m+2)-1)*(10^(s*(m+r+4))-1)/(10^(m+r+4)-1)+10^(m+2)-1) - 1 = [21.9(m).78.0(r)](s).21.9(m).77, where m, r and s are nonnegative integers and "." means concatenation and x(y) means x repreated y times.

If p=g(m,r,s) is prime, then 2*p is in the sequence.

This generalizes the above f(m,r) = [21.9(m-2).78](r)-1 = g(m-2,0,r-1), for r>0. Also a(4)=2*g(1,0,0), a(6)=2*g(2,0,0), a(7)=2*g(0,0,1), a(8)=2*g(4,0,0), a(10)=2*g(7,0,0), a(11)=2*g(0,4,1), a(12)=2*g(1,2,1) and a(13)=2*g(8,0,0). - Farideh Firoozbakht, Feb 14 2014

Links

Table of n, a(n) for n=1..13.

Example

sigma(21)=32=reversal(23)=reversal(21+2).

Mathematica

Do[If[c=FromDigits[Reverse[IntegerDigits[2+n]]]; c>n && DivisorSigma[1, n] == c, Print[n]], {n, 44000000}]

Crossrefs

Cf. A000203, A004086, A230009, A230768.

Sequence in context: A102018 A086947 A230768 * A101700 A275359 A022291

Adjacent sequences: A230018 A230019 A230020 * A230022 A230023 A230024

Keyword

nonn,base,more

Author

Farideh Firoozbakht, Dec 06 2013

Extensions

a(9)-a(10) from Giovanni Resta, Dec 13 2013

Status

approved