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%I #10 Mar 28 2015 18:06:37
%S 0,1,1,111,291,651,4251,165751,64101,78501,222501,62501601,62516001,
%T 62660001,2441447211,3922328562757,390625025601,2482366251,2851006251,
%U 62500000160001,390881000001,412041406251,15259444422501,40002500000001
%N a(n) is the smallest number m such that phi(10^n + m) = 10^n.
%C a(n) = A097649(n) - 10^n.
%C 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.
%C a(11) is greater than 5*10^7.
%F a[n_]:=(For[m=0, EulerPhi[10^n+m]!=10^n, 1=1, m++ ];m)
%e a(10)=222501 because phi(10^10+222501)=10^10 and for m < 222501 phi(10^10 + m) != 10^10.
%t a[n_]:=(For[m=0, EulerPhi[10^n+m]!=10^n, 1=1, m++ ];m);Do[Print[a[n]], {n, 0, 10}]
%t (* 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 *)
%Y Cf. A097649.
%K nonn
%O 0,4
%A _Farideh Firoozbakht_, Sep 05 2004
%E More terms from _Robert G. Wilson v_, Mar 14 2005
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