A358 Antoine Verroken

A358 Antoine Verroken

Q1.

111616 2^10 * 109 446464 2^9 * 872 447744 2^8 * 1749 566656 2^7 * 4427 877888 2^6 * 13717 881888 2^5 * 27559 944944 2^4 * 59059 999944 2^3 * 124993 999988 2^2 * 249997 999994 2 * 499997

Q2. La séquence A05338 de l'OEIS répond à la question

A053338 a(n) contains n digits (either '6' or '9') and is divisible by 2^n.

¹

6, 96, 696, 9696, 69696, 669696, 6669696, 96669696, 696669696, 9696669696, 69696669696, 969696669696, 9969696669696, 69969696669696, 969969696669696, 9969969696669696,

99969969696669696, 999969969696669696(list; graph; refs; listen; history; text; internal format)

OFFSET

_1,1

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n)=a(n-1)+10^(n-1)*(6+3*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n- 1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 6, if not then n-th term begins with a 9.