A224476 (2*16^(5^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 1.

6, 1, 251, 3751, 68751, 718751, 9218751, 24218751, 74218751, 8574218751, 13574218751, 663574218751, 5163574218751, 30163574218751, 980163574218751, 2480163574218751, 37480163574218751, 987480163574218751, 487480163574218751, 65487480163574218751

Offset: 1

Author

Eric M. Schmidt, Apr 07 2013

Keywords

• nonn
• base

Comments

a(n) is the unique positive integer less than 10^n such that a(n) + 2^(n-1) + 1 is divisible by 2^n and a(n) - 1 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 A063006. The other trimorphic numbers ending in 1 are included in A199685 and A224474.

Programs

Sage

def A224476(n) : return crt(2^(n-1)-1, 1, 2^n, 5^n)

Formula

a(n) = (A224474(n) + 10^n/2) mod 10^n.