[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A097650
a(n) is the smallest number m such that phi(10^n + m) = 10^n.
0
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.
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
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Sep 05 2004
EXTENSIONS
More terms from Robert G. Wilson v, Mar 14 2005
STATUS
approved