A222222 In the number n, replace all (decimal) digits '1' with '5' and vice versa.

0, 5, 2, 3, 4, 1, 6, 7, 8, 9, 50, 55, 52, 53, 54, 51, 56, 57, 58, 59, 20, 25, 22, 23, 24, 21, 26, 27, 28, 29, 30, 35, 32, 33, 34, 31, 36, 37, 38, 39, 40, 45, 42, 43, 44, 41, 46, 47, 48, 49, 10, 15, 12, 13, 14, 11, 16, 17, 18, 19, 60, 65, 62, 63, 64, 61, 66, 67, 68, 69, 70, 75, 72, 73, 74, 71

Offset: 0

Author

M. F. Hasler, Feb 12 2013

Keywords

• nonn
• base
• easy
• look

Comments

The map which is applied to primes in A171024.

Links

• Matthew L. LaSelle, Table of n, a(n) for n = 0..9999 (first 1000 terms from Alois P. Heinz)

Crossrefs

Cf. A222210-A222254; A171013-A171016, A175770, A171018-A171057.

Programs

Haskell

a222222 = foldl f 0 . map (read . return) . show :: Integer -> Integer
          where f v d = 10 * v + if d == 1 || d == 5 then 6 - d else d
-- Reinhard Zumkeller, Jan 29 2014

Maple

a:= proc(n) local m, d; d:=irem(n, 10, 'm');
     `if`(n=0, 0, parse(cat(a(m),`if`(d in [1, 5], 6-d, d))))
    end:
seq(a(n), n=0..99);  # Alois P. Heinz, Mar 02 2013

Mathematica

a[n_]:= IntegerDigits[n]/.{1->5, 5->1} // FromDigits; Table[a[n], {n, 0, 80}] (* Vincenzo Librandi, Jul 30 2013 *)

PARI

A222222(n,d=[0,5,2,3,4,1,6,7,8,9])=sum(i=1, #n=digits(n), d[n[i]+1]*10^(#n-i)) \\ gives correct value for n=0 iff d[1]=0, since digits(0)=[] in PARI (v.2.6)

Formula

Recurrence: a(10*n+i) = 10*a(n)+g(i) for 0 <= i <= 9, where

g(x) = -13/10080*x^9 +43/840*x^8 -611/720*x^7 +457/60*x^6 -57739/1440*x^5 +5007/40*x^4 -62231/280*x^3 +13941/70*x^2 -319/5*x. - Robert Israel, May 13 2014