OFFSET
1,1
COMMENTS
A prime p is a solution of reversal(x) - phi(x) = 1 iff p is a palindrome.
If p = 15*10^n-1 is prime then 38*p is in the sequence. The first three such terms are 38*(15*10^1-1)=a(4), 38*(15*10^2-1)=a(8), and 38*(15*10^15-1).
If p=25*10^m+1 is prime then 40*p is in the sequence.
The sequence A230020 gives composite solutions of equation sigma(x)-reversal(x)=1 and the sequence A130913 gives composite solutions of equation phi(x)+sigma(x)=2*reversal(x). - Farideh Firoozbakht, Nov 26 2013
[From Farideh Firoozbakht, Feb 07 2014] (Start)
Let f(s,m,r) = 10^(r*m+4r+s+2)+22*10^((s/2)+2)*(10^(m+2)-1)*(10^(r*(m+4))-1)/(10^(m+4)-1)+40, where s, m and r are nonnegative integers.
If p=f(s,m,r)/40 is prime then s>1 and f(s,m,r)=40*p is in the sequence.
If r=0 then f(s,m,0) = 10^(s+2)+40 = 1.0(s).40, where dot "." means concatenation and x(y) means the digit x is repeated y times.
If r>0 then f(s,m,r) is integer iff s is even. In that case, f(s,m,r) = 1.0(s/2).(21.9(m).78)(r).0(s/2).40.
Examples include a(5)=f(2,m,0)=10040, a(15)=f(2,0,1)=102178040, a(18)=f(9,m,0)=100000000040 and a(19)=f(4,1,1)=100219780040.
f(1970,19,19) is a 2410-digit term of the sequence. (End)
a(23) > 10^13. - Giovanni Resta, Aug 12 2019
EXAMPLE
reversal(52)-phi(52)=25-24=1.
MATHEMATICA
r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Do[c=r[n]; If[c<n && c-EulerPhi[n]==1, Print[n]], {n, 2100000000}]
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Farideh Firoozbakht, Apr 28 2007, Dec 03 2007
EXTENSIONS
a(17)-a(20) from Giovanni Resta, Oct 28 2012
a(21)-a(22) from Giovanni Resta, Aug 12 2019
STATUS
approved