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A007627 Primitive modest numbers.
(Formerly M4888)
2
13, 19, 23, 29, 49, 59, 79, 89, 103, 109, 111, 133, 199, 203, 209, 211, 233, 299, 311, 409, 411, 433, 499, 509, 511, 533, 599, 611, 709, 711, 733, 799, 809, 811, 833, 899, 911, 1003, 1009, 1011, 1027, 1033, 1037, 1099, 1111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Modest numbers (A054986) are the same but without assuming (a,b)=1.

For given k, (see FORMULA section) b's are divisors of (10^k - 1), and a's are co-prime with b, number of pairs (a,b) is sum(phi(b_i), i=1..m) -1 where b_i are divisors of (10^k - 1),

m = d(10^k - 1) the number of divisors of n (A000005),

and phi is Euler totient function (A000010).

E.g., for k = 1: b = 1, 3, 9, and pairs of (a,b) are:

(1,3), (2,3), (1,9), (2,9), (4,9), (5,9), (7,9), and (8,9 ) - total of 8 pairs. - Zak Seidov, Mar 22 2012

REFERENCES

Problem 1291, J. Rec. Math., 17 (No.2, 1984), 140-141.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

n = a*10^k + b such that (a, b)=1, n == a (mod b), a<b<10^k.

PROG

(Haskell)

import Data.List (inits, tails)

a007627 n = a007627_list !! (n-1)

a007627_list = filter modest' [1..] where

   modest' x = or $ zipWith m

               (map read $ (init $ tail $ inits $ show x) :: [Integer])

               (map read $ (tail $ init $ tails $ show x) :: [Integer])

      where m u v = u < v && (x - u) `mod` v == 0 && gcd u v == 1

-- Reinhard Zumkeller, Mar 27 2011

CROSSREFS

Cf. A054986, A055018.

Sequence in context: A191020 A180545 A113017 * A180525 A257590 A121877

Adjacent sequences:  A007624 A007625 A007626 * A007628 A007629 A007630

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

STATUS

approved

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Last modified April 27 11:04 EDT 2017. Contains 285512 sequences.