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A003595
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Numbers of the form 5^i*7^j with i, j >= 0.
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19
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1, 5, 7, 25, 35, 49, 125, 175, 245, 343, 625, 875, 1225, 1715, 2401, 3125, 4375, 6125, 8575, 12005, 15625, 16807, 21875, 30625, 42875, 60025, 78125, 84035, 109375, 117649, 153125, 214375, 300125, 390625, 420175, 546875, 588245, 765625, 823543, 1071875, 1500625
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = (5*7)/((5-1)*(7-1)) = 35/24. - Amiram Eldar, Sep 22 2020
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MATHEMATICA
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a = {}; Do[If[EulerPhi[35 k] == 24 k, AppendTo[a, k]], {k, 1, 10000}]; a (* Artur Jasinski, Nov 09 2008 *)
fQ[n_] := PowerMod[35, n, n] == 0; Select[Range[600000], fQ] (* Bruno Berselli, Sep 24 2012 *)
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PROG
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(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(7), N=7^n; while(N<=lim, listput(v, N); N*=5)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011
(Magma) [n: n in [1..600000] | PrimeDivisors(n) subset [5, 7]]; // Bruno Berselli, Sep 24 2012
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a003595 n = a003595_list !! (n-1)
a003595_list = f $ singleton 1 where
f s = y : f (insert (5 * y) $ insert (7 * y) s')
where (y, s') = deleteFindMin s
(Python)
from sympy import integer_log
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum(integer_log(x//7**i, 5)[0]+1 for i in range(integer_log(x, 7)[0]+1))
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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