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

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

Offset: 1

Author

Ctibor O. Zizka, Mar 30 2009

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A158520, A034887, A129344.

Programs

Magma

[n: n in [0..10^5] | Modexp(10, n, n+1) eq 0]; // Vincenzo Librandi, Mar 07 2018

Maple

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

Mathematica

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

PARI

is(n)=n=(n+1)>>valuation(n+1,2);ispower(n,,&n);n==1||n==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, N-1); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 12 2012

Formula

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

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