A224474 (2*16^(5^n) - 1) mod 10^n: a sequence of trimorphic numbers ending in 1.

1, 51, 751, 8751, 18751, 218751, 4218751, 74218751, 574218751, 3574218751, 63574218751, 163574218751, 163574218751, 80163574218751, 480163574218751, 7480163574218751, 87480163574218751, 487480163574218751, 5487480163574218751, 15487480163574218751

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) + 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. Corresponding 10-adic number is A063006. The other trimorphic numbers ending in 1 are included in A199685 and A224476.

Programs

Sage

def A224474(n) : return crt(-1, 1, 2^n, 5^n)

Formula

a(n) = (2 * A016090(n) - 1) mod 10^n.