A097650 a(n) is the smallest number m such that phi(10^n + m) = 10^n.

0, 1, 1, 111, 291, 651, 4251, 165751, 64101, 78501, 222501, 62501601, 62516001, 62660001, 2441447211, 3922328562757, 390625025601, 2482366251, 2851006251, 62500000160001, 390881000001, 412041406251, 15259444422501, 40002500000001

Offset

0,4

Comments

a(n) = A097649(n) - 10^n.

phi(10^0+0) = 0, phi(10^1+1)=10 and for n > 0, phi(10^(n+1) + 15*10^n) = 10^(n+1) so for each n, a(n) exists and is less than 25*10^(n-1) + 1. It seems that for n > 0, a(n) mod 10 = 1.

a(11) is greater than 5*10^7.

Links

Table of n, a(n) for n=0..23.

Formula

a[n_]:=(For[m=0, EulerPhi[10^n+m]!=10^n, 1=1, m++ ];m)

Example

a(10)=222501 because phi(10^10+222501)=10^10 and for m < 222501 phi(10^10 + m) != 10^10.

Mathematica

a[n_]:=(For[m=0, EulerPhi[10^n+m]!=10^n, 1=1, m++ ]; m); Do[Print[a[n]], {n, 0, 10}]
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := If[n == 0, 1, Block[{p = Select[ Divisors[10^n], PrimeQ[ # + 1] &]}, Min[ Transpose[ Partition[ Flatten[ Table[ Select[ Transpose[{Times @@@ KSubsets[p, i], Times @@@ KSubsets[p + 1, i]}], #[[1]] == 10^n &], {i, 9}]], 2]][[2]] ]]]; Table[ f[n] - 10^n, {n, 0, 23}] (* Robert G. Wilson v, Mar 19 2005 *)

Crossrefs

Cf. A097649.

Sequence in context: A180115 A082941 A029486 * A271312 A171773 A349951

Adjacent sequences: A097647 A097648 A097649 * A097651 A097652 A097653

Keyword

nonn

Author

Farideh Firoozbakht, Sep 05 2004

Extensions

More terms from Robert G. Wilson v, Mar 14 2005

Status

approved