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
Keywords
Examples
a(10)=222501 because phi(10^10+222501)=10^10 and for m < 222501 phi(10^10 + m) != 10^10.
Crossrefs
Cf. A097649.
Programs
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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 *)
Formula
a[n_]:=(For[m=0, EulerPhi[10^n+m]!=10^n, 1=1, m++ ];m)
Extensions
More terms from Robert G. Wilson v, Mar 14 2005
Comments