A053380 a(n) contains n digits '8' or '9' and is divisible by 2^n.

8, 88, 888, 9888, 89888, 989888, 9989888, 89989888, 989989888, 8989989888, 98989989888, 898989989888, 8898989989888, 98898989989888, 998898989989888, 8998898989989888, 98998898989989888, 898998898989989888, 9898998898989989888, 99898998898989989888, 999898998898989989888

Offset

1,1

Comments

It is somewhat nontrivial that the definition uniquely defines a(n). - M. F. Hasler, Feb 02 2026

Links

Ray Chandler, Table of n, a(n) for n = 1..1000

Formula

a(n+1) = a(n) + 10^n * (8 + [a(n)/2^n 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 an 8, if not then n-th term begins with a 9.

Prog

(PARI) first(n, t=0)=vector(n, k, t+=(8+(t%2^k>0))*10^(k-1)) \\ M. F. Hasler, Feb 02 2026

Crossrefs

Cf. A023415, A050621, A050622, A035014 (same with digits 3 & 4), A053312 - A053338 (digits 1,2 through 6,9) and A053376 - A053379 (1,8 through 7,8).

Sequence in context: A053379 A002282 A112907 * A250166 A247738 A115864

Adjacent sequences: A053377 A053378 A053379 * A053381 A053382 A053383

Keyword

base,nonn,easy

Author

Henry Bottomley, Mar 06 2000

Status

approved