%I #22 Apr 17 2017 04:58:16
%S 1320,1640,1768,1996,13200,16400,19984,19996,132000,164000,199996,
%T 1320000,1640000,1999936,13200000,16400000,16666240,17999488,18515584,
%U 19999984,19999996,132000000,164000000,164296960,166662400,199999936,199999984,1320000000
%N Composite numbers n such that n - phi(n) is a power of 10.
%C Numbers n such that n - phi(n) is a positive power of 10.
%C Numbers n such that phi(n) = n - 10^floor(log(10,n)).
%C The most significant digit of all terms is equal to 1, since all terms are even and for even numbers n, phi(n) <= n/2.
%C If p = 5^(2n-1)*10^m-1 is prime then s = 4^n*p is in the sequence, because s - phi(s) = 10^(2n+m-1).
%C For n=1,2, ..., 6, ... smallest such term of the sequence respectively are 1996, 19984, 1999936, 1999999744, 19999999998976,19999999995904, ... .
%C Sequence A248858 gives number of digits of these terms.
%H Giovanni Resta, <a href="/A248857/b248857.txt">Table of n, a(n) for n = 1..47</a> (terms < 10^12, first 41 terms from Robert G. Wilson v)
%e 1320 is in the sequence because 1320 - phi(1320) = 10^3.
%t a248857[n_] := Select[Select[Range@n, CompositeQ[#] &], IntegerQ[Log10[# - EulerPhi[#]]] &]; a248857[10^7] (* _Michael De Vlieger_, Jan 07 2015 *)
%o (PARI) lista(nn) = forcomposite(n=2, nn, if (ispower(n-eulerphi(n),,&d) && (d==10), print1(n, ", "))); \\ _Michel Marcus_, Jan 06 2015
%Y Cf. A000010, A067206, A066663, A244440, A248854, A248858.
%K nonn
%O 1,1
%A _Farideh Firoozbakht_, Dec 31 2014
%E a(22)-a(28) from _Giovanni Resta_, Apr 17 2017