

A158911


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


4



0, 1, 3, 4, 7, 9, 15, 19, 24, 31, 39, 49, 63, 79, 99, 124, 127, 159, 199, 249, 255, 319, 399, 499, 511, 624, 639, 799, 999, 1023, 1249, 1279, 1599, 1999, 2047, 2499, 2559, 3124, 3199, 3999, 4095, 4999, 5119, 6249, 6399, 7999, 8191, 9999, 10239
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OFFSET

1,3


COMMENTS

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


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000 (first 134 terms from Peter Pein)


FORMULA

a(n) = A003592(n)  1.


MAPLE

N:= 20000: # to get all terms <= N
sort([seq(seq(2^i*5^j1, j=0..floor(log[5]((N+1)/2^i))), i=0..ilog2(N+1))]); # Robert Israel, Mar 06 2018


MATHEMATICA

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


PROG

(PARI) is(n)=n=(n+1)>>valuation(n+1, 2); ispower(n, , &n); n==1n==5 \\ Charles R Greathouse IV, Jan 12 2012
(PARI) list(lim)=my(v=List(), N); lim++; for(n=0, log(lim)\log(5), N=5^n; while(N<=lim, listput(v, N1); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 12 2012
(Magma) [n: n in [0..10^5]  Modexp(10, n, n+1) eq 0]; // Vincenzo Librandi, Mar 07 2018


CROSSREFS

Cf. A158520, A034887, A129344.
Sequence in context: A069183 A119907 A241335 * A086772 A301767 A169898
Adjacent sequences: A158908 A158909 A158910 * A158912 A158913 A158914


KEYWORD

easy,nonn


AUTHOR

Ctibor O. Zizka, Mar 30 2009


EXTENSIONS

Corrected by Claudio Meller, Rick L. Shepherd, Charles R Greathouse IV and R. J. Mathar, Aug 23 2010
Edited by N. J. A. Sloane, Aug 25 2010, Oct 04 2010


STATUS

approved



