A322131 In the decimal expansion of n, replace each digit d with 2*d.

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 210, 212, 214, 216, 218, 40, 42, 44, 46, 48, 410, 412, 414, 416, 418, 60, 62, 64, 66, 68, 610, 612, 614, 616, 618, 80, 82, 84, 86, 88, 810, 812, 814, 816, 818, 100, 102, 104, 106, 108, 1010, 1012, 1014

Offset: 0

Author

Rémy Sigrist, Nov 27 2018

Keywords

• nonn
• base
• easy
• look

Comments

This is an operation on digit strings: 1066 becomes 201212, for example. 86420 becomes 1612840. The result is always even - see A330336. - N. J. A. Sloane, Dec 17 2019

This sequence is a variant of A124108 in decimal base.

Examples

			For n = 109:
- we replace "1" with "2", "0" with "0" and "9" with "18",
- hence a(109) = 2018.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A048385, A061581, A066686, A124108, A330336.

Programs

Maple

f:= proc(n) option remember;
local m,d;
d:= n mod 10; m:= floor(n/10);
if d >= 5 then 100*procname(m) + 2*d
else 10*procname(m)+2*d
fi
end proc:
f(0):= 0:
map(f, [$0..100]); # Robert Israel, Nov 28 2018

Mathematica

a[n_] := FromDigits@Flatten@IntegerDigits[2*IntegerDigits[n]]; Array[a, 60, 0] (* Amiram Eldar, Nov 28 2018 *)

PARI

a(n, base=10) = my (d=digits(n, base), v=0); for (i=1, #d, v = v*base^max(1,#digits(2*d[i],base)) + 2*d[i]); v

Python

def A322131(n):
   return int(''.join(str(int(d)*2) for d in str(n))) # Chai Wah Wu, Nov 29 2018

Formula

A061581(n+1) = a(A061581(n)).

A066686(a(n), a(k)) = a(A066686(n, k)) for any n > 0 and k > 0.

a(10*n + d) = 10*a(n) + 2*d for any n >= 0 and d = 0..4.

a(10*n + d) = 100*a(n) + 2*d for any n >= 0 and d = 5..9.

G.f. g(x) satisfies g(x) = (2*x + 4*x^2 + 6*x^3 + 8*x^4 + 10*x^5 + 12*x^6 + 14*x^7 + 16*x^8 + 18*x^9)/(1-x^10) + (10 + 10*x + 10*x^2 + 10*x^3 + 10*x^4 + 100*x^5 + 100*x^6 + 100*x^7 + 100*x^8 + 100*x^9)*g(x^10). - Robert Israel, Nov 28 2018