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A248857 Composite numbers n such that n - phi(n) is a power of 10. 3
1320, 1640, 1768, 1996, 13200, 16400, 19984, 19996, 132000, 164000, 199996, 1320000, 1640000, 1999936, 13200000, 16400000, 16666240, 17999488, 18515584, 19999984, 19999996, 132000000, 164000000, 164296960, 166662400, 199999936, 199999984, 1320000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that n - phi(n) is a positive power of 10.

Numbers n such that phi(n) = n - 10^floor(log(10,n)).

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.

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).

For n=1,2, ..., 6, ... smallest such term of the sequence respectively are 1996, 19984, 1999936, 1999999744, 19999999998976,19999999995904, ... .

Sequence A248858 gives number of digits of these terms.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..47 (terms < 10^12, first 41 terms from Robert G. Wilson v)

EXAMPLE

1320 is in the sequence because 1320 - phi(1320) = 10^3.

MATHEMATICA

a248857[n_] := Select[Select[Range@n, CompositeQ[#] &], IntegerQ[Log10[# - EulerPhi[#]]] &]; a248857[10^7] (* Michael De Vlieger, Jan 07 2015 *)

PROG

(PARI) lista(nn) = forcomposite(n=2, nn, if (ispower(n-eulerphi(n), , &d) && (d==10), print1(n, ", "))); \\ Michel Marcus, Jan 06 2015

CROSSREFS

Cf. A000010, A067206, A066663, A244440, A248854, A248858.

Sequence in context: A023318 A066663 A067206 * A260839 A157266 A069737

Adjacent sequences:  A248854 A248855 A248856 * A248858 A248859 A248860

KEYWORD

nonn

AUTHOR

Farideh Firoozbakht, Dec 31 2014

EXTENSIONS

a(22)-a(28) from Giovanni Resta, Apr 17 2017

STATUS

approved

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)