A248854 -id:A248854 - cp's OEIS frontend

A248857 Composite numbers n such that n - phi(n) is a power of 10.

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

Offset: 1

Farideh Firoozbakht, Dec 31 2014

nonn

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.

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

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

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

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

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

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

A248856 Numbers n such that n + pi(n) is a power of 10.

Original entry on oeis.org

1, 853, 91182, 926756, 9374193, 94535668, 951496285, 9563906973, 963706466000, 9665127969899, 96891533076641, 970995550452370, 9728143518403637, 97441817594570206, 975843062833251485, 9771174122943813068

Offset: 1

Farideh Firoozbakht, Dec 31 2014

Numbers n such that pi(n) equals 10^ceiling(log(10,n)) - n.
853 is the only known prime term of the sequence. If n is a prime term of the sequence and m = pi(n) then prime(m) + m is a power of 10. So 147 = pi(853) is the only known number m such that prime(m) + m is a power of 10. What is the next such number?
For each number n there exists at most one n-digit term.
a(11) = 96891533076641 is also prime. - Chai Wah Wu, May 25 2018

			pi(96891533076641) + 96891533076641 = 10^14 so 96891533076641 is in the sequence.

Cf. A000720, A244440, A248854.

Select[Range[1000], IntegerQ[Log[10, # + PrimePi[#]]] &] (* Alonso del Arte, Dec 31 2014 *)

for(n=1,10^3,s=digits(n+primepi(n)-1);if(s==[]||vecmin(s)==9,print1(n,", "))) \\ Derek Orr, Jan 02 2015

a(12)-a(16) from Chai Wah Wu, May 25 2018

cp's OEIS Frontend

A248857 Composite numbers n such that n - phi(n) is a power of 10.

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