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A158911 Numbers of the form 2^i*5^j - 1. 4

%I

%S 0,1,3,4,7,9,15,19,24,31,39,49,63,79,99,124,127,159,199,249,255,319,

%T 399,499,511,624,639,799,999,1023,1249,1279,1599,1999,2047,2499,2559,

%U 3124,3199,3999,4095,4999,5119,6249,6399,7999,8191,9999,10239

%N Numbers of the form 2^i*5^j - 1.

%C Numbers n such that 10^n is divisible by n+1.

%C Numbers n such that the prime divisors of n+1 are also divisors of the numbers m obtained by the concatenation of n and n+1. For example, for n=39, m = 3940, the divisors of 40 are {2, 5} and the divisors of 3940 are {2, 5, 197}. - _Michel Lagneau_, Dec 20 2011

%C The entries correspond to positional information of A156703, which stem from ratios of consecutive integers. For example, A156703(4)=875 yields a(5). This is because 875 was produced from n/(n+1) where n=7, i.e., 7/8 = 0.875. Similarly, a(23)=399 stems from 399/400=0.9975 (A156703(22)). - _Bill McEachen_, Jan 05 2014

%H Robert Israel, <a href="/A158911/b158911.txt">Table of n, a(n) for n = 1..10000</a> (first 134 terms from Peter Pein)

%F a(n) = A003592(n) - 1.

%p N:= 20000: # to get all terms <= N

%p sort([seq(seq(2^i*5^j-1, j=0..floor(log[5]((N+1)/2^i))),i=0..ilog2(N+1))]); # _Robert Israel_, Mar 06 2018

%t fQ[n_] := PowerMod[10, n, n + 1] == 0; Select[ Range[0, 11000], fQ] (* _Robert G. Wilson v_, Sep 08 2010 *)

%o (PARI) is(n)=n=(n+1)>>valuation(n+1,2);ispower(n,,&n);n==1||n==5 \\ _Charles R Greathouse IV_, Jan 12 2012

%o (PARI) list(lim)=my(v=List(), N); lim++; for(n=0, log(lim)\log(5), N=5^n; while(N<=lim, listput(v, N-1); N<<=1)); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jan 12 2012

%o (MAGMA) [n: n in [0..10^5] | Modexp(10, n, n+1) eq 0]; // _Vincenzo Librandi_, Mar 07 2018

%Y Cf. A158520, A034887, A129344.

%K easy,nonn

%O 1,3

%A _Ctibor O. Zizka_, Mar 30 2009

%E Corrected by _Claudio Meller_, _Rick L. Shepherd_, _Charles R Greathouse IV_ and _R. J. Mathar_, Aug 23 2010

%E Edited by _N. J. A. Sloane_, Aug 25 2010, Oct 04 2010

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Last modified April 22 18:24 EDT 2021. Contains 343177 sequences. (Running on oeis4.)