A224477 (5^(2^n) + (10^n)/2) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 5.

0, 75, 125, 5625, 40625, 390625, 7890625, 62890625, 712890625, 3212890625, 68212890625, 418212890625, 4918212890625, 9918212890625, 759918212890625, 1259918212890625, 6259918212890625, 756259918212890625, 7256259918212890625, 42256259918212890625

Offset: 1

Author

Eric M. Schmidt, Apr 07 2013

Keywords

• nonn
• base

Comments

a(n) is the unique nonnegative integer less than 10^n such that a(n) + 2^(n-1) - 1 is divisible by 2^n and a(n) is divisible by 5^n.

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Trimorphic Number
• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A033819. Converges to the 10-adic number A018247. The other trimorphic numbers ending in 5 are included in A007185, A216093, and A224478.

Programs

Sage

def A224477(n) : return crt(2^(n-1)+1, 0, 2^n, 5^n)

Formula

a(n) = (A007185(n) + 10^n/2) mod 10^n.